Philip Gould, who advises the Prime Minister on public opinion, and Stan Greenberg, who does the same job for President Clinton, have held monthly strategy meetings in Israel for the past two years with Mr Barak, the new Israeli Prime Minister. Confidential documents seen by The Independent reveal the extent of their work in helping the Israeli Labour Party back to power.
Mr Barak even came to London for a two-day session on how to remodel his image.
The White House yesterday hailed the election of Mr Barak with restrained delight but was closer to the election campaign than its public neutrality suggested.
Two other members of the team credited with helping Mr Clinton to his first presidential victory in 1992, James Carville and Robert Shrum, worked with Mr Greenberg on strategy, opinion polls and advertising for Mr Barak.
The possibility of a new advance in the Middle East is especially welcome in Washington, where President Clinton is in sore need of a foreign policy success to counter the diplomatic setbacks in Kosovo. "Because of his military service, the question of General Barak's devotion to the security of Israel is not in question," President Clinton told reporters yesterday after meeting King Abdullah of Jordan.
The direct involvement of Blair and Clinton aides followed an appeal for help by Daniel Levy, the Tel Aviv-based son of Lord Levy, a friend and the tennis partner of Mr Blair.
Mr Gould and Mr Greenberg were the architects of the proposal that the party change its name, even suggesting at one point that it be called New Labour. In the event, the Labour Party kept its name but fought the election under the One Israel banner, the name of the alliance it formed with two smaller parties.
How much of a difference the new model Labour Party made to the outcome of the election is doubted by some Israeli analysts. Mr Barak won, they believe, because so many of Mr Netanyahu's colleagues had been fired or deserted and set up the Centre Party to remove him. Mr Barak's strategy amounted to keeping his mouth shut and watching his opponent self-destruct.
When they became involved in 1997, Mr Gould and Mr Greenberg warned that the modernisation of Labour was the most important and difficult task facing the Barak campaign. They recommended the "dramatic high risk" strategy pursued by Mr Blair on, for example, the ditching of Labour's Clause IV.
At first they thoughtLabour's prospects were poor. The party's combination of "elitism plus softness on the core security issues" was summed up as "fatal". Mr Gould and Mr Greenberg warned that Labour was not considered to be "the party of the people"; the party that could best resolve social problems or unite the country.
Last night Mr Gould said most of the credit should go to Mr Greenberg, a partner in his London-based political consultancy. "Stan did an extraordinary job. He kept faith during a difficult project and got an incredible result."Reuse content