WASHINGTON – Prime Minister Blair is poised to be more critical of President Bush and may press to be repaid for his past support from Britain, even if it places strain on Anglo-American relations, British political sources say.

Mr. Bush’s re-election win was greeted with horror by much of the British press, with the Daily Mirror, a left-wing newspaper, asking the bald question on its front-page yesterday: “How can 59,054,087 people be so dumb?”

The tone of the fallout may give Mr. Blair little choice but to take a harder stance against Mr. Bush, sources say.

As far as the White House is concerned, Mr. Blair will remain a reliable ally during Mr. Bush’s second term, but the imperatives of British politics are likely to complicate White House foreign policy and force Mr. Bush to make difficult choices between assisting an ally or tempering aspects of his own approach to the war on terror.

Mr. Blair faces severe domestic challenges. They include an election in the spring, when Mr. Blair will confront an electorate that deeply dislikes Mr. Bush, and mounting dissent within his own Labor Party, much of it tied to the war in Iraq.

According to Blair advisers and Labor politicians, the British leader’s close ties to Mr. Bush have become an increasing electoral liability, and a Kerry win would have simplified life for Mr. Blair, liberating the prime minister from a relationship that has poisoned links with his own party and made him highly unpopular in Britain.

Some in Mr. Blair’s inner circle were rooting for Mr. Kerry on Tuesday night, and when exit polls suggested Senator Kerry would likely win the presidential contest, there was a wave of relief in Downing Street, say British political sources. It is unclear whether Mr. Blair himself hoped for a Democratic win, although some Labor sources in London say he saw both candidates as representing mixed blessings.

A Kerry win would have left the British leader isolated over Iraq, but it would have helped him repair relations with his own center-left party.

“He expected Bush to win, but it is not entirely what he wanted,” a senior politician in Mr. Blair’s Labor Party told The New York Sun. “But a Kerry win would have had its drawbacks, too.”

Mr. Blair’s former spokesman, Alastair Campbell, acknowledged just before balloting that Mr. Blair’s close alliance with Mr. Bush had caused the prime minister “enormous political difficulties,” although he insisted the British leader was well prepared to be able to work with whoever won the election.

Labor politicians now fear Mr. Bush’s re-election win has robbed Mr. Blair of a chance to heal party divisions. Peter Kilfoyle, a former defense minister, said the election result represented a “poisoned chalice” for the prime minister. “A break in the presidency would have given him the opportunity to redirect himself,” he said.

A prominent Labor opponent of the Iraq War, Alice Mahon, said her party colleagues are worried. “Bush is back with a stronger mandate than ever and Tony Blair is his biggest cheerleader. He has got to start putting daylight between himself and Bush.”

In the days before and after the presidential election, Mr. Blair has gone out of his way to assuage party critics. The prime minister has told Cabinet colleagues that he believes a second Bush term will be different from the first, with a greater readiness by the White House to repair transatlantic relations and to act in a more multilateral way.

Members of Mr. Blair’s inner circle have been assuring Labor politicians that Mr. Bush will be “more mellow” and that the prime minister now has the ability to sway Mr. Bush. His former spokesman, Mr. Campbell, said in one TV interview midweek that “uniquely among world leaders, Tony is in a position to exercise influence and leverage.”

Mr. Blair served notice publicly on Wednesday in a speech from his Downing Street office that he indeed expects some rewards from Mr. Bush, foremost among them a White House commitment to revitalize the stalled Middle East peace process and a readiness to cooperate on climate change.

Downing Street sources say Mr. Blair has a personal pre-election guarantee from Mr. Bush that he will take a more active approach to resolving the Israel-Palestine conflict, and they say they were pleased to hear Mr. Bush talking about the Middle East in his press conference yesterday.