President Bush will bid Britain farewell today and then fly home after a frantic final tour of Europe where he secured vague assurances of support, but little tangible progress, for what remains of his foreign policy.

Downing Street is already playing down expectations for today’s talks with Gordon Brown, suggesting that their discussions would be “general in nature” and are unlikely to yield any specific agreements.

Although Mr Bush promises that he will “sprint to the finish” with an ambitious agenda for his last six months, officials privately acknowledge that the President is running into the sand – and out of time.

Yesterday No 10 and the White House sought to quash reports of divisions over Iraq, the invasion of which five years ago has defined Mr Bush’s presidency.

The Observer claimed that Mr Bush had delivered a “stern message” to Mr Brown against a precipitate withdrawal of British troops, and quoted the President as saying: “I am confident that he, like me, will listen to our commanders to make sure that the sacrifices that have gone forward won’t be unravelled by drawdowns.”

Mr Bush last night played down suggestions that he was worried that Britain would pull out its forces prematurely although he indicated that he and Mr Brown had not always communicated well. He said, in an interview with Sky News: “The worst thing allies can do is not communicate about our plan and our desires. We all want to take troops out of Iraq and we are. He, by the way, left a lot of troops in, more so than they thought they were going to leave in initially. And so we communicate now and, if there’s success, we’ re going to pull troops out, and I have absolutely no problem how Gordon Brown is managing the Iraqi effort.”

Downing Street was similarly anxious to stamp on any suggestion of a split, saying that Mr Brown was not interested in setting “arbitrary time-tables”.

But officials pointed out that the Government would make a “monitoring” statement to Parliament before the summer and another in the autumn. In practice, diplomats say they will be discussing any further troop reductions with John McCain and Barack Obama, the candidates vying to be the next occupant of the Oval Office.

Along with much of the world, Mr Brown is beginning to look beyond Mr Bush and, while keen to maintain a rather stiff frienship with the President, he has resisted the intense embrace in which Tony Blair was clutched.

Mr Hadley said: “Obviously, Brown is a different personality than Blair. The President, I think, has forged a good, close relationship with each and both of them.”

He sought to rebut an article in The Times last week suggesting the United States was getting more support from President Sarkozy in France, a country Mr Bush now describes as “America’s first friend”, saying: “The United States and Britain continue to have a very special relationship.”

David Cameron, who angered Washington two years ago by using the anniversary of 9/11 to criticise what he called a “slavish” relationship between Britain and America, is expected to have private talks with Mr Bush today.

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