The man demonised by many in the country at large as well as at Westminster is characteristically charming. Michael Gove is also disarmingly humble.

In this most personal of interviews, a rueful Gove says for the first time that it was 'wrong' for him to have stood in the bitter Tory leadership contest last summer, confirms for the first time that his old friend David Cameron is not speaking to him after Brexit, which Gove masterminded, and says 'I'm a sinner and I know it profoundly.'

We start, though, with Donald Trump, famously interviewed last month by Gove in the Times, for whom the former Cabinet minister writes while serving as the – now – backbench MP for Surrey Heath.

If Gove was too 'soft' on Trump in the interview, as some have claimed, he is not afraid to go on the attack on this occasion. The new president is 'narcissistic' and 'egotistical' enough to try and see out a full term, Gove says, but he is likely to lose the next election and, sensing that, Trump may quit early. Further, for all his support among white evangelicals, Trump is 'the least influenced by religion American president' since Nixon.

And despite Gove being seen as a 'neo-conservative' who Kenneth Clarke said would 'go to war with at least three countries at once', this undeniably thoughtful politician is surprisingly critical of Trump's 'sectarian' ban on travel, migration and asylum from seven Muslim-majority countries.

On whether Trump could quit early, Gove, a keen observer of American politics, says that impeachment is unlikely because of the arithmetic in the Senate. 'But there's a broader question – does he have the character to see it through? On the one hand he is someone who is clearly narcissistic or egotistical enough to want to be seen as a success, and therefore he'll want to show his critics that he can meet this challenge. On the other hand though there is just a sheer unpredictability about the way in which he sometimes responds to events, that it would be impossible I think to predict with accuracy.

'My hunch is that he will see through this term and then he will lose the next election. Knowing that he might lose, he might find some means of quitting while he thinks he is ahead, though I suspect that his ego will mean he will both want to see what he can do in office and he will believe that he can prevail against whoever the Democrat opponent is.'

Asked whether he approves of the travel ban, he says: 'No, I don't think it's the right thing to do. I think that as a matter of...broad principle I think it is legitimate for America that it thinks, and indeed is legitimate for the president to say that he thinks that certain people are not conducive to the public good and all the rest of it. But I think there are three problems with the travel ban: one problem is that it follows on from his commitment to have a ban on Muslims coming into the country, so any form of travel ban that looks as though it's sectarian, has problems from the beginning. The second thing is that even though the countries to which it applies are either countries which are wracked by civil war or which have significant Islamic fundamentalist forces within them, nevertheless it looks inconsistent because there are some other countries [such as Pakistan and Saudi Arabia which should be included].

'The third thing is that the manner in which it was implemented, and the uncertainty of for example people who had green cards or people who had been interpreters who had worked in Iraq with American forces meant that it seemed at once crude and unfair. So for all of those reasons I think it was wrong. That's not to say that a Trump administration or someone in the future couldn't come up with approaches towards restricting access to the US that some people might think were wrong but which I could see the case for, but as implemented and as conceived I think it was wrong.'

Trump was elected with massive support from evangelicals, particularly white evangelicals. Does Gove believe that Trump is influenced by Christians? 'Well, it's a very interesting question because I think that he's probably one of the American presidents least influenced by religion for a long time. Barack Obama was influenced by his own personal faith. George W Bush ditto. Bill Clinton, even though there were all sorts of character and ethics issues, was clearly influenced by his faith; Ronald Reagan ditto; George H W Bush a particular type of episcopalian; Jimmy Carter clearly. I think you'd probably have to go back to Richard Nixon to find an American president who was less influenced by their faith than Donald Trump.

'The second thing is that even though Mike Pence,  the Vice President, is clearly someone who is very heavily influenced by his faith, if one looks more broadly at the people who [Trump] has appointed, he's tended to appoint people on the basis of either business expertise or military expertise or rather than coming from particular traditions. So it is curious. And normally one of the criticisms that's been directed at the Republican party is that a particular set of policies and assumptions have come from a particular evangelical standpoint and that's influenced the Republican party unduly, but we're now in the curious position where one of the least popular – not only in his own country but in the world – Republican presidents is someone who is further away from that tradition than anyone in the last 30 years.'

If Gove is typically articulate on US politics, he is unusually tongue-tied when asked, lastly on Trump, why he failed to mention that the Times proprietor Rupert Murdoch was present at the interview conducted by Gove, Murdoch's favourite politician and, doubtless, columnist.

Gove is careful not to confirm or deny Murdoch's presence. 'I haven't said anything about who was and wasn't in – um,' – he trails off. 'The best thing to say I think, in fairness is, um [long pause] in securing the interview, I think the fact that it was the Times newspaper and the fact that we had the - what's the word...I think [pause] it's probably better for me not to go into how the interview arose or how it came about but I think it's entirely fair for people to make a set of conclusions or assumptions about that. I won't comment on them if you don't mind...I haven't said anything about it at this stage.'

Turning to British matters, Gove is 'broadly' happy with the way Brexit is panning out, but its architect is more than ever keen to show that he feels the pain of the 48 per cent who voted for Britain to stay in the EU. 'I mean I recognise of course that there are still lots of people obviously who voted and argued for Remain who feel anything from disorientated to devastated to still finding it difficult to come to terms with things. I think overall however, that the PM's handling it well, I think the outlook is broadly reassuring and optimistic...'

Gove is hopeful that Brexit acceptance is setting in. 'I think there is an opportunity – I hope it's there – that the Article 50 Bill – it'll face challenges in the Lords – but I hope there is an opportunity for people to say OK, it's happening now, let's concentrate on the type of Brexit that we should have and the type of new relationship that we should have in the future rather than hoping that we can have a re-fight of it.'

On Tuesday night, Gove took part at an event at Speaker's House, hosted by John Bercow, at which the Labour MP Hilary Benn spoke on the future of Brexit and Gove responded. 'One of the impressive things about Hilary was the way that, while not for a moment retreating from his belief that we should still be in the EU, he also acknowledged the validity of the result and then went on to engage with how the values – belief in internationalism chief among them – which had led him to support remain should influence how Brexit operated.'

Talking of Labour figures, Gove is known to admire Tony Blair. What does he make of the former prime minister's recent intervention calling on remainers to fight back? Boris Johnson dismissed Blair as a warmongerer and called on people to 'rise up' and switch him off their television screens.

Gove, in contrast, confirms that he admires Blair. 'I disagreed with the overall thrust of his speech. But I do admire him. You can't read the speech and not think this is someone who has political gifts and intellectual power, and even if I think much of what he said was misconceived, I think as an ex PM he has a right to make his case. As I say I disagreed with him on it – but...Blair's record I think, in the future, will be, it'll be balanced. I think people will have a balanced view of it. At the moment I think Blair has suffered from an excessive level of enthusiasm early on in his premiership, and then subsequently not just Iraq but also his post politics business activities. I think there are legitimate criticisms that can be directed at him both as a politician and in the way that he has conducted some of his business activities, but you have to weigh against that the fact of someone who has devoted himself to public service for a considerable part of their career and achieved some very good things, so I think that taking a couple of steps back, while I disagree with him on this issue he is entitled to his view and respect for it.'

On the Tory leadership last summer, Gove explains why he decided to stand, having previously agreed to run Boris Johnson's campaign. Gove's move, which was described by Rachel Johnson, Boris's brother, as that of a 'suicide bomber,' stunned Westminster, though some suspect he planned it all along. So when did he decide to run and what was the deciding factor?

'In a nutshell, I hadn't thought and I hadn't anticipated on running. I had thought -- maybe this was foolish -- that if the country voted to leave that David Cameron would not immediately stand down. And he did. I didn't myself want to run, and Boris after some – you know, he reflected on it – I thought it was better for the country to have someone who had advocated to leave the the EU to be presented to the country a that point. I thought that Boris had fought well during the campaign and deserved the chance to run.

'However, in the days that followed there were a number of things that happened that made me increasingly worried that while Boris was – is – an enormously talented figure, he wasn't the right person to be prime minister. I sort of then - on the...night before nominations had to go in – talked to some friends. A number of things had happened which had shaken my confidence in Boris's candidacy – not fundamentally altered my view of him as a good person – but had shaken my confidence that he was the right person to be prime minister at that time. And then having decided that I didn't think he was the right person I then thought well, if we're going to have someone who had advocated to leave then I'll put myself forward.

'With the benefit of hindsight, I should have not been so quick to say that I was going to support Boris in the first place and' – here Gove pauses, and takes a deep breath – 'probably should never have run myself. But anyway, after what happened, I think probably the right result for the country emerged in that I think that having in Theresa May someone who had advocated Remain but was determined to honour the result was actually best in terms of bringing the Conservative party back together after what had been a difficult period. I also think that her particular style, experience and so on meant that she's handled events over the course of the last eight months better I think than I would have done, and I think any of the other candidates would have done.'

Staying on Cameron, the two men's relationship is worth exploring, because – unlike Johnson and Cameron – Gove and the former Tory leader were genuine friends, with Gove, a lifelong eurosceptic, having persuaded Cameron to stand for the leadership in 2005 from a position to the right of one of the then favourites, the pro-European Kenneth Clarke.

Gove laughs at the claim that he 'invented' Cameron, and then expands on a comment he has made before about speaking now only to one of Johnson and Cameron. Again though, he adopts an uncharacteristically hesitant tone. 'I've spoken to Boris. Again, um, David – the opportunity hasn't arisen, and my view is that...what's the right thing to say? Yes, I think David was a great prime minister, I think he achieved a great deal. I think he has every right to feel that [pause] the way in which things turned out in the end...give him the right to feel, well, you know, I didn't necessarily...get the recognition or the appreciation that everything I have put into this job necessarily deserves, so my view is that I entirely respect his right to...have left Parliament, devote himself to other causes outside Parliament, and...make judgments himself about how he spends his time and who he talks to and I don't make any criticism.'

On Gove's own future in Parliament, he says he has no plans to stand down as an MP, and adds that he enjoys – almost – all aspects of the job. 'I think I'll stay in Parliament for as long as people will have me. I certainly enjoy at the moment almost all -- not all -- almost all of the aspects of being a Member of Parliament. And you know it's a great privilege. It might be that at some future point people might grow exasperated with me or I find that my interest and appetite for being here fades but at the moment I am enjoying it so I am happy to carry on through thick and thin for a few years yet.'

Some talk of this Murdoch favourite as a future Times editor. But Gove is clear: 'No, I wouldn't really want to do that, no. No. I think that there are certain things that could happen which would mean – I mean I would never want to tempt fate or anything like it – there are certain things that could happen which would mean that I might want to leave Parliament, but no, I am concentrating at the moment on, certainly writing – I love writing – but operating as an MP.'

Finally, we turn to faith. It may surprise some that Gove, who has a Greek Orthodox icon prominently displayed on his House of Commons desk, is a firm believer who regularly worships in church. To those who don't know him, Gove 'came out' as a Christian in a lengthy Spectator article at Easter 2015. But in fact, he has all his life been a believer. 'I was brought up as a member of the Church of Scotland, and my mother is a still regular churchgoer. My father never really had any strong religious beliefs [but] I was brought up as a Christian.'

Asked what are his Christian influences now, Gove is reflective. 'I think that there are a variety of things...I think that – it may seem like an eccentric thing to say – I enjoy listening to sermons and homilies, and it may be a consequence of having grown up in the Church of Scotland where the sermon is almost the centrepiece in a way that obviously the Eucharist or the Mass is in the Catholic – small or large 'C' – tradition.

'But I remember that when I grew up there was a minister in the church that I attended with my mother that was a chap called Douglas Sutherland, and he was a brilliant preacher and subsequent to that, there have been individuals some of whom I've heard talk even though I have never attended their church, that I have found inspirational. So for example, I have never been to Holy Trinity Brompton, but [the HTB vicar] Nicky Gumbel I've heard speak and I think that he's outstanding.

'I've also heard [the Bishop of London] Richard Chartres – again he comes from a very different tradition – and I think that he is a fantastic preacher. Separately, even though again I'm not a Roman Catholic, I've occasionally gone to the Brompton Oratory specifically because Fr Julian Large who is a former contemporary friend of mine when he worked at the Telegraph, is now in charge of the Oratory there, is again a great preacher. And there are individual... Christian writers as well who have had a significant influence on me, and I suspect that the greatest would probably be CS Lewis. I think that again some people find his approach not to their taste but I think that in terms of Christian apologetics I think he's fantastic.

'And there's only one other thing that I would say, which is that I was at an event with Matthew Barzun, the now outgoing American Ambassador [to the UK], and he recommended a book by Dorothy L Sayers called The Mind of the Maker which he said was the best work of the Christian apologetics that he'd read, and it was interesting that he was so enthusiastic about it, and I love Dorothy L Sayers's fiction so...I've got a copy of it.'

As we draw to a close, Gove – often accused of 'betrayal' and of being 'ruthless' – again shows humility: 'While at different times the strength of my faith has wavered or been tested, and while I would never say that anyone should' – he laughs – 'look at any of the things that I've done and say this is a pattern of Christian living – because I am a sinner and I know it profoundly -- nevertheless, I have held throughout to a belief in Christian doctrine, and while I worship now in a Church of England church rather than a Church of Scotland church, my views I would say were those of – and again it's always very difficult to pigeon hole, to define oneself – but of a straightforward, mainstream, Protestant Christian.'

Follow James Macintyre on Twitter @James_Macintyre.