Justin Welby has opened up about how his own failings make him angry and said that he spends "a lot of time feeling a fraud" in a personal and at times emotional interview at the Greenbelt Christian festival in Northamptonshire.

Speaking to the 'vicar of Gogglebox', television star Kate Bottley in front of hundreds of festival-goers, the Archbishop of Canterbury said that wherever he went he found people who could do his job "infinitely better" than he could.

And in surprisingly frank comments about same-sex relationships, Welby said that he "can't see the road ahead" for the Church.

Before the banter-filled question and answer session, Welby was introduced by Christian Today's Andy Walton who said: "One of [our guests] is the most high profile Christian in the country... and the other is the Archbishop of Canterbury".

The Archbishop joked that "the fact that I'm Archbishop of Canterbury is one of the things that makes me seriously doubt the infallibility of God."

Welby said "there is only one way to overcome" the self-doubts, "and that's prayer and the Bible – it's being part of the family of Christ... with all kinds of problems and issues and you've got a role in that family".

The Archbishop told of a visit last week to the Demelza hospice in Canterbury, of which he is patron and where he was showed around by an eight-year-old blind boy. An emotional Welby described sitting with with the parents of  a young boy who had died, and told of how, having asked the parents if they wanted him to pray, he did not know what to say until words came to him. "Jesus, this is all wrong," he prayed. "We shouldn't be here."

Welby said that when his own seven-month-old daughter died in a car-crash, "God just showed up. We can never remember a time when He was closer... It felt like the Lord just reached out and took her. It was that real."

Asked by Bottley what his "biggest frustration" was and what made him angry, Welby said: "Me. That's the thing I get most angry about – me... My own failings." The Archbishop, who praised his "wonderful" staff, gave the example of "when I get narked with people and show it," adding: "I have to not send emails a lot... The best friend of Christian unity is the draft box". He told of how he sleeps on some emails and shows them to others before sending them, and said that he no longer monitors Twitter because "if [what people write about me] is nice you get a bit up yourself and if it's nasty you get cross and either way you have to repent".

Welby joked that one of the nastiest things he had been called on Twitter was the "deputy anti-Christ – that really got to me: why am I the deputy? Talk about adding insult to injury."

He said that he found it "overwhelming" to address the crowd at Greenbelt, but frequently drew applause from the largely progressive audience.

Asked by an audience member who was due to enter a civil partnership when the Church would be in a position to bless the union, the Archbishop simply said that he did not know. "I don't have a good answer to it," he said. "If we were the only Church here and [there were] no other Churches, and if division didn't matter it would be much easier to answer".

Welby said that the inclusion of gay people and safeguarding against abuse were the two issues which he lies awake thinking about at night.

"Do I know when there will be a point when the blessing [of the civil partnership] will happen? No. I don't and I can't see the road ahead". He added that the Church started from a traditionalist position, moved on to out of touch and then "vicious" and "now we just look odd".

He said "we have to find a way to love and embrace everyone who loves Jesus Christ" but he added that this included people who feel – or come from societies which believe – that same-sex relationships are "deeply, deeply wrong".

Welby talked of an "incredible clash that is so important to so many people and goes to the heart of the identity of so many people". He added: "There isn't a simple solution... I haven't got a good answer." To applause, he said "I am constantly consumed with horror" at the way in which the Church has treated the gay community.

Asked about the dangers of ego in the job, Welby said: "You start assuming that things will happen without you asking all the time and that can get dangerous, really dangerous".

On the press, he said: "Oh, I've stopped worrying about that... I hate to say this but I quite like a lot of them," adding that he increasingly likes politicians who often "do an incredibly difficult job".

He went on: "The future of the Church is resurrection... The future of the Church in this land is amazing because God is God – he's not going to turn away. He will make sure that the name of Jesus is proclaimed in this land come what may."