Mr Cameron claimed that the new Prime Minister “can’t be the change that Britain needs”.

He added: “I think people should have the opportunity for change – people should be able to vote for change. That’s why we believe that there should be a general election straight away.

“Gordon Brown doesn’t have the mandate, he wasn’t elected as Prime Minister and he should go to the country.”

Critics warn that Mr Brown’s record at the Treasury gives a chilling indication of the direction of his new Government. Tightening household budgets – with another crippling interest rate rise almost certain next week – will contribute to a growing sense of unease.

Even Mr Brown, in his final months as Chancellor, admitted that slower economic growth and dwindling funds for crumbling public services lie ahead. His accession to power made a stark contrast with Mr Blair’s optimistic entry into Downing Street 10 years ago.

Under a grey, drizzly sky, Mr Brown delivered a brief speech about his plans for “a new Gov­ernment with new priorities”.

And he referred to his school motto from his childhood days at Kirkcaldy High, saying: “I will try my utmost.”

But there was no flag-waving welcome or cheering crowds of bused-in party supporters seen when New Labour first came to power in 1997.

With only his wife Sarah at his side, Mr Brown smiled once after pleas from press photographers.

In Mr Blair’s former private office, Mr Brown was last night finalising his first Government reshuffle.

The Cabinet is due to be unveiled at lunchtime today, with junior ranks of ministers – including a number of non-party peers and advisers – announced tomorrow. Earlier yesterday, Mr Brown was applauded by Treasury civil servants gathered in Whitehall before heading to Buckingham Palace.

In his last act as Chancellor, he signed paperwork confirming Mr Blair’s departure from the House of Commons. He spent nearly an hour in private talks with the Queen, formally accepting her invitation to form a Government and informing her of some of his plans.

He was driven to the Palace in a red Government Vauxhall – but returned in a new black, armour-plated Government Jaguar.

Arriving in Downing Street, he said: “This will be a new Gov­ernment with new priorities and I have been privileged to have been granted a great opportunity to serve my country.

“At all times, I will be strong in purpose, steadfast in will, resolute in action in the service of what matters to the British people, meeting the concerns and aspirations of our whole country.”

Mr Brown invoked his Scottish childhood in the Fife town of Kirkcaldy, when he said: “I grew up in the town I now represent in Parliament. I went to the local school. I wouldn’t be standing here without the opportunities I received there.

“I want the best of chances for everyone. That is my mission, that if we can fulfil the potential and realise the talents of all our people then I am absolutely sure that Britain can be the great global success story of this century.”

Mr Brown – who was accused of being a “Stalinist” control freak as Chancellor – claimed to have “listened and learned from the British people during a tour of the country.

“I have heard the need for change,” he said.

He promised to focus on improving hospitals and schools, pledged to build new homes to provide “affordable housing” and vowed to restore the trust in Government shattered during Blair’s years. “This need for change cannot be met by the old politics so I will reach out beyond narrow party interest. I will build a Government that uses all the talents.

“I will invite men and women of goodwill to contribute their energies in a new spirit of public service to make our nation what it can be.

“And I am convinced that there is no weakness in Britain today that cannot be overcome by the strengths of the British people.

“On this day, I remember words that have stayed with me since my childhood, my school motto...I will try my utmost. This is my promise to all of the people of Britain and now let the work of change begin.”

Mr Brown was last night congratulated by a series of world leaders.

He had a 10-minute “cordial and constructive” introductory conversation with George Bush.

He also spoke to French President Nicolas Sarkozy, German Chancellor Angela Merkel and Irish premier Bertie Ahern.

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