And former foreign secretary Margaret Beckett told the BBC it was "madness" to suggest the party needs a new leader.
"Gordon Brown is one of the most brilliant politicians of this or any generation, if he can't steer us through this, no-one can," she said.
A BBC survey of local Labour Party chairmen and women, meanwhile, suggests most back Mr Brown to lead the party into the next election, but there is unhappiness with the direction he is taking the party on public services.
And 25% of the 135 chairmen and women surveyed thought Mr Brown should have held an election last Autumn.
The survey - which contacted 38% of local Labour Party leaders - found 70 of them thought the party had become too close to big business.
Some 89 of the 135 chairmen and women thought Mr Brown was not right to encourage more private investment in the NHS.
Olympics Minister Tessa Jowell later told BBC 4's The World At One: "The Labour Party will always tend to be further to the left than a Labour government.
"A New Labour government has to govern from the centre and that means measuring the impact and the benefits of change in terms of what is achieved rather than the old way of thinking about this, which is that public is good and private is bad."
'Unlucky prime minister'
But former Liberal Democrat leader Paddy Ashdown - who was last year offered the Cabinet post of Northern Ireland secretary by Mr Brown - said he doubted the prime minister could survive.
On this unhappy anniversary friends will mutter, foes will shout about the prime minister's misjudgements
He told Straight Talk with Andrew Neil on BBC News: "I have made some mistakes in my life but viewed out from a year ago, it does not seem to me that my decision to decline Mr Brown's kind invitation to join his government was one of them.
"Can he survive? Well, Margaret Thatcher was more unpopular than him but does he, you know? She had the personality, the opportunity and the luck.
"He's an unlucky prime minister, he hasn't got a great personality and I can't see what the opportunity is."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.