Mr Blair became the representative of the Middle East Quartet – the UN, EU, US and Russia – a few weeks after leaving Downing Street. Last week, he visited the region for what he said was the 90th time since being appointed in June 2007. He spends one week a month based in Jerusalem or globetrotting on behalf of the Quartet. His office is funded by the Quartet members and his 24-hour security detail is on secondment from Scotland Yard but he receives no direct salary.

After four years of renting 15 rooms at the American Colony Hotel for his full-time staff, Mr Blair put down more permanent roots in 2011 by renting the penthouse of a new office building in Sheikh Jarrah, East Jerusalem.

But senior Palestinian officials and analysts told The Independent the move was unnecessary – his sojourn in the region should be cut short. "The Quartet has been useless, useless, useless," Mohammed Shtayyeh, an aide to the Palestinian President Mahmoud Abbas, said last week. He suggested that its constant need to reach internal consensus among its warring participants had rendered it ineffective.

"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, who had just ended 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'," he said.

Mr Shtayyeh is not alone. Last February, the Saban Centre for Middle East Policy at The Brookings Institution pronounced the body already dead in a report bluntly entitled The Middle East Quartet: A Post-Mortem.

"The Quartet has little to show for its decade-long involvement in the peace process. Israelis and Palestinians are no closer to resolving the conflict, and in the few instances in which political negotiations did take place, the Quartet's role was usually relegated to that of a political bystander," said the report. "Having spent most of the last three years in a state of near paralysis, and having failed to dissuade the Palestinians from seeking UN membership and recognition in September 2011, the Quartet has finally reached the limits of its utility.

"The current mechanism is too outdated, dysfunctional, and discredited to be reformed. Instead of undertaking another vain attempt to 'reactivate' the Quartet, the United States, the European Union, United Nations, and Russia should simply allow the existing mechanism to go quietly into the night," the report concluded.

Mr Blair rarely travels to Gaza, citing security reasons. The Quartet website features a number of achievements in the West Bank, including the removal of Israeli army checkpoints and upgraded facilities for exports. Palestinian and Israeli officials told The Independent that the Quartet appeared to be taking credit for other people's work.

"I think in general Palestinians are disappointed by the performance of the Quartet," said Ghassan Khatib, vice-president of Birzeit University near Ramallah and a former Palestinian Authority cabinet minister. "I cannot think of any serious thing that the Quartet succeeded to help us in.

"Sometimes Tony Blair speaks about removing checkpoints, but I think Israel was going to remove these checkpoints with or without the Quartet," said Dr Khatib. He said the Quartet's announcements about assisting the Palestinian economy were as hollow as their political achievements, but he stressed that his attitude wasn't personal. "It has nothing to do with Tony Blair … I think it's the Quartet that failed to deliver."

Mr Blair's Jerusalem office did not respond to a request for a comment.

Timeline: Blair's peace-making

June 2007

Tony Blair appointed Middle East envoy on behalf of the EU, US, UN and Russia.

May 2008

Launches peace plan for Israel-Palestinian conflict based on improving economic co-operation.

March 2009

On a visit to Gaza, Mr Blair calls on Israel to ease its blockade.

September 2011

Mr Blair warns that a bid for statehood at the United Nations by the Palestinian President Mahmoud Abbas would be "deeply confrontational".

October 2011

Nabil Shaath, one of the senior aides to President Abbas, has harsh words for the Palestinian leader, accusing him of talking "like an Israeli diplomat".