Tony Blair was the most successful – and the most controversial – Labour prime minister in UK history. After his party's years in the wilderness he swept to power in 1997 and went on to win two more elections. Among his domestic achievements was peace in Northern Ireland, a huge prize.

It's his foreign policy, however, which continues to define his time in office. His wars in Afghanistan and Iraq have led to calls for him to be regarded as a war criminal, though he continues to argue that invading Iraq was "the right thing to do".

Nevertheless: as soon as he stepped down as prime minister in 2007, he was appointed to a significant role in the Middle East. Blair became the representative of the 'Middle East Quartet' of the US, EU, UN and Russia, with offices and staff in Jerusalem and London. It was hoped that he would bring his formidable political skills to bear on the most intractable international problem of modern times: Israel-Palestine.

He has just resigned. A Quartet statement pays tribute to his "unwavering commitment to the cause of Israeli-Palestinian peace" and says he has made "lasting contributions to the effort to promote economic growth and improve daily life in the West Bank and Gaza".

The statement is very carefully worded. It acknowledges Blair's commitment to peace, but stops short of claiming he has actually achieved anything towards it. It is more positive about improvements to growth and daily life in the West Bank and Gaza, but it is far from triumphalist.

So what, if anything, has Blair achieved during more than 10 years of engagement in the region, and how will he be remembered there?

The Quartet was first established in 2002 and was designed to help promote the peace process between Israelis and Palestinians by means which included reforming Yasser Arafat's Palestinian Authority and creating economic growth. Blair was appointed as its Special Envoy in succession to James Wolfensohn, a former head of the World Bank, who resigned only a few months later because he believed he lacked the necessary political freedom to act.

Blair, however, believed he could make a difference, mainly through improving conditions for the Palestinians, who were being strangled by Israeli blockades, checkpoints and trade restrictions.

His mandate from the Quartet was fourfold. He was to:

– Mobilize international assistance to the Palestinians

– Help secure international support in addressing the institutional governance needs of the Palestinian State

– Develop plans to promote Palestinian economic development, including private sector partnerships, and

– Liaise with other countries as appropriate in support of the agreed Quartet objectives.

His office has a list of achievements impressive at least for its length. For instance, since 2007 many roadblocks have been removed, making for significant improvements in movement for people and goods. Bethlehem has been opened up, with tourist buses allowed to use more crossings. The site also hails improvements to the functioning of the Palestinian police force and many achievements in the economic area involving private investment aimed at creating jobs and infrastructure.

In spite of all this, Blair's time in the Middle East is being widely described as a failure. An open letter last June signed by pro-Palestinian activists including his own former international development secretary, Clare Short, urged his removal from office, saying: "It is our view that, after seven years, Mr Blair's achievements as envoy are negligible, even within his narrow mandate of promoting Palestinian economic development. Furthermore, the impression of activity created by his high-profile appointment has hindered genuine progress towards a lasting peace."

It said that after seven years there were still more than 500 checkpoints and roadblocks in the West Banks, that the Gaza strip remained in a state of crisis and that Israel continued to build illegal settlements. It quoted the former Palestinian Authority chief negotiator, Nabil Shaath, as saying that Blair has "achieved so very little because of his gross efforts to please the Israelis." The letter also questioned the transparency of his business dealings, saying he was accused of "blurring the lines between his public position as envoy and his private roles at Tony Blair Associates and the investment bank JPMorgan Chase" – for which he is a paid consultant.

Blair's office hit back, saying: "These are all people viscerally opposed to Tony Blair with absolutely no credibility in relation to him whatsoever. Their attack is neither surprising nor newsworthy. They include the alliance of hard right and hard left views which he has fought against all his political life. Of course he completely disagrees with them over the Middle East. He believes passionately in the two-state solution, but also believes that can only be achieved by a negotiation with Israel."

Its statement categorically denied any conflict of interest, saying: "Mr Blair has done no work for JPMorgan in the Middle East – he is the chair of their International Advisory Council – where he provides advice on global political issues."

Yet the open letter does reflect the concerns of many observers. In a nutshell: Blair didn't spend enough time on the job (less than a week a month); his business interests were confusingly close to his political role (denied); he was too close to Israel, and eight years after his appointment peace is no nearer and the two-state solution is dead in the water. 

Rev Phil Hill, a former lecturer at the Nazareth Evangelical Theological Seminary, tells Christian Today that during his five years in Israel, Blair was hardly mentioned in the media. "Jewish friends generally wondered what he did with his time. He was certainly not politically significant with regarrd to the peace process," he says. He recalls: "My Arab friends dismissed Blair as too pro-Jewish to be an honest broker of any peace initiative," adding: "Similarly, friends from the churches of the West Bank dismissed him as a non-event in terms of the peace process."

For Jeremy Moodey, chief executive of Embrace the Middle East, Blair's resignation was "long overdue". "There were too many unanswered questions about his record on the Iraq war and the apparent conflict of interest between his role as Quartet Envoy and his extensive business interests in the Middle East.

"He was also distrusted by the Palestinians, one of whose negotiators famously described the whole Quartet idea, and Blair's mission, as "useless, useless, useless" because of his refusal to confront Israel with the true reality of its occupation."

He was referring to Mohammed Shtayyeh, an aide to Palestinian President Mahmoud Abbas, who said that the Quartet's constant need to reach consensus among its four members had hamstrung it. "Always the statement of the Quartet really means nothing because it was always full of what they call constructive ambiguity that really took us to nowhere," said Mr Shtayyeh after a meeting with Mr Blair. "You need a mediator who is ready to engage and who is ready to say to the party who is destroying the peace process 'You are responsible for it.'"

In Shtayyeh's eyes – and in Moodey's – that party is Israel. Moodey says: "It would be unfair to blame Blair for the lack of any progress towards a negotiated settlement between Israel and the Palestinians in the nearly eight years since he was appointed. That is because it was mission impossible in the first place, given Israel's rejectionism and its refusal to end its occupation and negotiate genuinely towards a two-state solution.

"With no true Israeli vision for peace, Blair's mission and the whole Quartet project were doomed from the very start."

Who's to blame for the failure of the peace process depends very much on who you ask, with pro-Israel voices pointing to the continued Hamas menace – though Israeli President Benjamin Netanyahu's rejection of a two-state solution before the recent election still represents a crushing blow to hopes of a resolution.

However, not everyone is as negative about Blair's achievements. Jonah Agus, a research student at King's College, London, wrote for the Daily Telegraph that Blair's stint was "rather quiet". While he had little if any effect in Gaza, Agus says: "The West Bank, however, has remained relatively calm and Israel has eased movement for Palestinians by dismantling a number of checkpoints. The Palestinian National Authority has become more capable and certain sectors of the economy have seen rapid growth. Mr Blair also promoted the development of several new industrial parks, some of which have been brought to fruition."

He also notes that the West Bank has remained relatively stable. "As a result – and according to the remit of the Quartet Representative – Mr Blair's record in the West Bank has certainly been more productive."

What's emerged clearly from the announcement of Blair's departure is the visceral nature of the reactions to it. Social media was awash with vitriol, with one Twitter user, Matt Owen, suggesting that he "resigned because he wanted to spend more time with his demons". Another, Tiernan Douieb, said that he was stepping down "in order to spend less time ruining families". Columnist George Monbiot made an ironic reference to the FIFA controversy.

 Clearly for many people Tony Blair is directly and personally responsible not only for the Iraq war but for everything that followed from it, making an honest and factual assessment of his achievements very difficult.

It's also obviously true that his explicit support for Israel has not played well with pro-Palestinians – though given his remit of encouraging economic growth and support for the Palestinian Authority, which could only be achieved with Israeli support, he could argue that antagonising Israel could only be counter-productive.

In the end, it seems fairest to say that Blair's limitations were the limitations of the Quartet, and of the whole international effort to bring peace to Israel-Palestine. That is further away than ever.