The election of Barack Obama as US President will bring about "fundamental change in America's relationship with the rest of the world", Foreign Secretary David Miliband said today.

Mr Miliband said that the handover of power in Washington would have "big and positive" effects for Britain, ushering in a foreign policy agenda which chimed with the UK's priorities of reform for international institutions, action on climate change and progress in the Middle East.

His comments came as Prime Minister Gordon Brown promised to work with the president-elect on a "progressive" agenda to build a fairer global society.

Mr Brown said that US voters had shown they back the belief, shared by Mr Obama and the Labour Government, in the duty of government to intervene to help families and businesses during the current economic downturn.

But shadow foreign secretary William Hague interpreted the Democratic senator's victory differently, arguing it showed the appetite for "change" among electorates around the world.

Mr Miliband told BBC1's Andrew Marr Show: "The result of Tuesday's election isn't just a realignment within American politics, it also heralds fundamental change in America's relationship with the rest of the world.

"I think that will have big and positive effects for Britain."

Without drawing a direct contrast with the administration of George Bush, Mr Miliband made clear he expects Mr Obama's foreign policy approach to differ radically from that of his Republican predecessor.

"He is an instinctive multi-lateralist," said the Foreign Secretary. "He is clear that issues of the environment and climate change as well as issues of security are at the heart of foreign policy.

"He has also made clear that he understands that there is a new world out there and you can't run the world from the G7 countries, you have to fashion a global settlement that includes the Chinas and Indias of this world, but also the developing countries.

"I think that that gives us the opportunity to refashion international institutions and the approach to foreign policy in a very fundamental way."

Last week's election was "a turning point in America's relationship with the rest of the world", said Mr Miliband, adding: "It creates an agenda of reform - reforming international institutions, reforming America's relationship with the Arab world and the Middle East, reforming the image of America.

"In the end, that is important for all of us because America is the leader of a grand coalition of countries that are committed to values of democracy, human rights and personal freedom. That's something we need to see spread and I think Obama's administration will do that."

He warned that the lesson from Mr Bush's administration was that "you can't wait until year seven to get really stuck into the Palestinian issue" and voiced hope that Mr Obama will engage with the Middle East peace process "from day one".

And he added: "I see, from what president-elect Obama has said, shared values with the British Government. I see a shared agenda in terms of Afghanistan, Pakistan, the Middle East, climate change, but I also see some shared insights about what works in foreign policy in the modern world."

In an article for The Observer, Mr Brown wrote: "The people of America made their choice last week. They picked a progressive president, inspiring the world with their belief that in difficult times people need their government to ensure more - not less - help and security is available for families and business.

"I'm looking forward to cooperating with the president-elect in building a new global society in which the advancement of people - their homes, jobs, savings and pensions - is always put first."

But Mr Hague told Sky News' Sunday Live that Mr Obama's victory showed people had a "real desire" for change.

"It's a huge change of course in American politics," said Mr Hague.

"It's always, I think, quite difficult to extrapolate from one country to another. I think the only common theme in politics the world over is people are crying out for change in different ways."

Mr Hague pointed to yesterday's general election in New Zealand, in which the long-standing Labour government was swept out by a Conservative opposition, the National Party.

He said: "People certainly have a real desire for change - Barack Obama really personified that.

"I think what may have changed the world over is that people will listen again to the USA; that the US has an opportunity now to greatly improve the impression it makes on the rest of the world."