Tony Blair was the opening act at this week's glittering gala celebration in Jerusalem, paying tribute to President Shimon Peres, who will soon turn 90. Kicking off an evening of song, dance and praise, Blair told the audience of 2,000 Israeli and international politicians, celebrities, diplomats, business people and academics: "We in Britain have our Queen, you have your Shimon."

It was a relatively rare public appearance by the British former prime minister, who has deliberately kept a low profile since he became Middle East envoy in June 2007. And, although his job is to help the Palestinians create the foundations of a future state and improve their economy, it's hard to imagine him saluting the Palestinian president, Mahmoud Abbas, just a few miles away in Ramallah, in quite the same way as he paid tribute to Peres.

Six years almost to the day after he left Downing Street and became the Quartet's Middle East representative – and after recently chalking up his 100th trip to the region – Blair has a mixed report card. Allies point to a string of concrete economic gains, but critics say that little of real substance has been achieved.

"It's unfortunate that such a brilliant man with a past record of friendship with the Palestinian people has achieved so very little because of his gross efforts to please the Israelis," said Nabil Shaath, a senior Palestinian official who has been vocal in his criticisms of Blair.

Shaath's comments were echoed by Hanan Ashrawi, a veteran of peace negotiations. "Frankly speaking, there are no tangible achievements – apart from maybe his frequent flyer points," she said, adding: "Blair has an instinctive sympathy for the Israeli perspective. His first impulse is to present Israel's point of view."

Palestinian suspicions may be reinforced by acclaim for Blair from Danny Ayalon, Israel's former deputy foreign minister. "With his calibre and his record, Blair was the right man for the job," he said. "Because he had the name and the record, and also the political acumen, he has done the job in a magnificent way. He has a lot to show in what he has achieved so far."

Praised or disparaged, Blair's role may now be on the verge of significant expansion as the US secretary of state, John Kerry, makes the biggest push in years to get the Middle East peace process back on track. Last month, Kerry announced a $4bn package to help the Palestinian economy – a drive to be led by Blair. Implementation, however, is presumably contingent on progress on the political track, about which many are deeply sceptical.

Blair got the job as Quartet envoy on the day he left Downing Street in June 2007. The position was seen by some as a gift from President George W Bush for Britain's loyal backing for the US invasion of Iraq. When in office, Blair urged Bush to press for a resolution of the Israeli-Palestinian conflict as a quid pro quo for the UK's support. Now the former prime minister had his chance.

According to Toby Greene, the author of a new book, Blair, Labour and Palestine, and research director at the pro-Israel organisation Bicom, "Blair saw the [Quartet] role as a continuation of the principles he had espoused as prime minister. He saw the Israeli-Palestinian conflict as an important part of the war on terror, and believed it provided a rallying call to extremists. Resolving it would take away the opportunity it gave extremists to recruit others to their cause."

This, along with Palestinian grievances, was Blair's prime motivation in taking the job, said Greene.

Constrained by a tightly worded remit, Blair was thrust into the minutiae of Palestinian state-building – to the relief of the Israelis, who wanted him kept out of the broader political process.

Robert Danin, the Quartet's head of mission in Jerusalem from 2008 until 2010, now with the Council on Foreign Relations in Washington, said: "Blair had a limited mandate to work on the economic track while the US took the lead on the political track. Tony has respected that division of labour."

The Washington-based Brookings Institution last year said the remit was "far too narrow, fragmented and detached from the political process to have any meaningful impact". In an analysis paper, The Middle East Quartet: A Post-Mortem, it added: "Blair, a quintessentially political figure, resisted public calls, and perhaps his own inclinations, to play a more overtly political role and instead has remained loyal to his narrow economic mandate."

The Palestinians say that Blair's limited focus on economic rejuvenation has come at the expense of political progress towards an independent state and so served Israel's interests.

"If you don't have political power, why should anyone listen? Cosmetic changes in the occupation don't get us anywhere," said Ashrawi. "We don't want to make our prison more comfortable, we want to get out of the prison. Without occupation we can build a thriving and vibrant economy and a 21st-century state. But under occupation we can only go so far before the walls of our cells close in on us."

According to Shaath, "there can be no separation between the political and the economic – and the political is paramount. Without seeing the political implications, you go nowhere in your economic effort. That's what we tried to explain to Blair very early in the game – to no avail."

Ayalon said such criticism was misplaced. "It's coming from self-serving narrow political motives. The Palestinians wanted to politicise the economic help, and Blair did not play their tune," he said. And a European diplomatic source who has observed Blair's work closely over the past few years said: "Achieving peace was never in his mandate. He was never going to come here and solve it."

Blair's office dismisses the mandate issue as a red herring, saying it is irrelevant to the mission's actual achievements. Among these, say officials, are double-digit growth in the Palestinian economy, lifting checkpoints that severely restricted movement in the West Bank, assisting the development and training of Palestinian security forces, the easing of Israel's blockade on Gaza in 2010, securing an additional 10,000-plus permits for Palestinian labourers to work in Israel, and persuading Israel release a share of the radio spectrum to allow a second mobile phone company to operate in Palestine.

The Brookings report acknowledged "concrete improvements on the ground". But their value is disputed.

"Blair spent a year negotiating the removal of 12 checkpoints, and in the meantime [Israel] built another 36," said Ashrawi. "It's an exercise in futility."

Shaath said: "I don't want to rob Blair of any credit, but nothing he did is irreversible by the Israelis. Nothing structural has changed."

That view is supported by a World Bank report published in March, which warned that economic gains overseen by Blair are at risk of being reversed without political progress. "Palestinian institutions have the required capacity to exercise state functions but Israeli-imposed economic restrictions continue to constrain sustainable economic growth. This situation is unlikely to change as long as political progress remains absent," it said.

There are also differences in views of the easing of Israel's blockade of Hamas-ruled Gaza. One of those involved in "very labour-intensive" negotiations said it was to Blair's lasting credit that the policy was changed to allow more goods to enter the blockaded territory. But Shaath was dismissive: "'Easing' instead of 'ending' is the key word for the Israelis. Eased can be un-eased at will. It's still under their total control. Blair went along with what the Israelis wanted."

When Blair has strayed into the political arena, critics say it has been to Israel's advantage. Almost two years ago, he made intensive efforts to dissuade Palestinian leaders from taking their bid for recognition of the state of Palestine to the UN. At the time, Shaath denounced Blair as "Israel's defence attorney" and the Palestinians said he was "unwelcome" in the Palestinian territories due to his "clear bias towards Israel".

Some Palestinian politicians have accused Blair of not condemning harshly enough Israel's continued expansion of illegal settlements in the West Bank, and its restrictions, evictions and demolitions in the 62% of the West Bank under full Israeli control.

This is vigorously rejected by Blair's office, which points to frequent statements it has issued. Blair allies say such criticism is based on "gesture politics", and point out that it comes from the Palestinian political elite, for whom small economic improvements are less relevant than for ordinary workers, business people and their families.

In the end, said Danin, the former head of mission, Blair's record speaks for itself . "Banging fists on the table might make you feel good but it's not going to produce results. Some in the international community would like to see Tony beat up the Israelis but it wouldn't lead to any real results. Blair has been very effective."

But, said the European diplomatic source, Palestinian criticism was "not entirely unfair".

"The impression among Palestinians is that Blair has been used by Israel. He has leverage, and he hasn't used it. Why not? He's too conservative with a small c, and he sees the situation too instinctively from a US-Israeli point of view. Obviously he intellectually understands the Palestinian perspective, but his gut is with Israel and the US."