TONY BLAIR now knows who will be in the White House for the rest of his time as Prime Minister. By a strange symmetry, we now have two term-limited leaders, one voluntary and the other by the US Constitution. George W. Bush’s second term will cover the same period, up to January 2009, that Mr Blair has said he wants to stay in Downing Street.

But talk yesterday of there being no change misses the point. Yes, there will be continuity. But elections change expectations. No longer can the European and British Left regard Mr Bush’s presidency as an aberration. His margin in the popular vote on an increased turnout was decisive.

Mr Blair has invested a lot in his links with Mr Bush. He likes and trusts him. Yet in the eyes of many, the relationship has been one-way traffic. The Faustian bargain which Mr Blair entered into with Mr Bush during 2002 — supporting the Iraq war in return for involving the United Nations and a US pledge to press for a Middle East settlement — has produced meagre returns with a violent and unstable Iraq.

Tuesday’s election provided both an opportunity and a necessity for Mr Blair to change the relationship. The opportunity is because of what Mr Bush owes Mr Blair, as shown by the many references to the Prime Minister during the campaign. If ever there is a time for Mr Blair to seek a sympathetic hearing from Mr Bush, it is now.Moreover, Mr Blair's advisers point out that the second terms of US presidents, such as Ronald Reagan, are often very different from their first terms, since they no longer have to seek votes.

The necessity is because of the unpopularity in Britain of Mr Bush. This is not a question of “distancing”, which the Blairites rightly dismiss as self-indulgent gesture politics. Rather, Mr Blair needs to demonstrate in public that he is not “Bush’s poodle”. He is not. But some of Mr Blair’s advisers have worried that he has been too much of a believer. Many hoped that a Kerry victory might tone down Mr Blair’s “neocon” side.

Mr Blair has been discussing his post-election agenda with Sir Nigel Sheinwald, his main foreign policy adviser, and Sir David Manning, Sir Nigel’s predecessor and the British Ambassador in Washington. The immediate challenges are to ensure that the Iraqi elections go ahead in late January, that the fragile democracy in Afghanistan is consolidated, and to tackle the growing threat of the Iranian nuclear programme.

But Mr Blair’s main post-election priority, as he said in his Labour conference speech in October, is reviving talks on the Israeli-Palestinian dispute. At the time, this sounded like one of his familiar “I will solve the world’s problems” type of promise. These have often fallen flat in the past because of a lack of commitment from Washington. Moreover, Britain’s involvement with the Palestinian Authority has caused considerable friction with the Bush Administration, most recently when Sir Nigel Sheinwald headed a delegation of British foreign policy and intelligence officials in secret talks in Washington in July.

But, on the basis of recent contacts with Mr Bush, Mr Blair now believes that the President is genuine about investing political capital in the Middle East peace process. There is an opening after last week’s vote by the Knesset to approve Israel’s withdrawal from Gaza. Much will depend on Yassir Arafat’s health. But policymakers are already considering big questions about whether Britain and other European countries should be more directly involved in guaranteeing the security of Gaza.

Yet the close Bush-Blair links also threaten Mr Blair’s aim of taking a leading position in the EU, a danger which he does not appreciate. The US is likely to come first, as before. Jacques Chirac will not be alone in Europe in using the re-election of Mr Bush as justification for creating a distinctive European pillar in competition with the US. This “multi polar” approach is rejected by many new EU entrants as well as by Britain. But a continued Bush presidency may not only further divide Europe but also leave Britain adrift in the mid-Atlantic.

The trickiest question for Mr Blair is whether he will continue to suffer politically from his closeness to Mr Bush. It will not be possible to draw a line under the Iraq war, as some hoped if John Kerry had won — although Mr Blair has been spared the taunts from the Left of being isolated and associated with electoral failure.

The Blair camp will claim that Mr Bush’s victory shows that the Iraq war is not necessarily electorally damaging. That may be wishful thinking. But one certain result of the election is that Mr Blair’s fate and his foreign policy will remain inextricably linked to Mr Bush.

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