Senior Cabinet ministers have endorsed Gordon Brown as the inevitable successor to Tony Blair.
Gordon Brown is widely tipped to succeed Tony Blair
But the chancellor could face union opposition, after vowing to continue the Prime Minister's public services reform programme if elected leader.
Speaking at the start of the Labour Party's conference, Work and Pensions Secretary David Blunkett said there was "no obvious alternative" to Mr Brown.
Peter Hain said he could not "see anyone wanting to stand against him".
"Gordon is so far out in front of anyone else, he is one of the twin architects, with Tony Blair, of Labour's most successful period," the Northern Ireland Secretary said.
The prime minister has said he will not stand for election as leader again, but has refused to say when he would step down.
'Reform at home'
Mr Blair has always said his third term as party leader would be "unremittingly new Labour" and he is determined to push ahead with change in industry, health, education and welfare.
In a message to Labour party members arriving for the conference, Mr Blair said the programme of reform must be "accelerated" and that public services could not survive "simply by them being free".
He has also stressed that the UK needs to meet the challenges of the new global economy.
Many to the left in the Labour party have hoped a Brown leadership succession would put a stop to what the left-wing Campaign Group dubbed Mr Blair's "scorched earth" agenda.
And union leaders have misgivings about the proposed extension of private sector involvement in the public services.
But Mr Brown has said: "The programme of reform will continue when Tony steps down because it is the right programme for Britain.
"Indeed it is the only programme for Britain if we are going to compete in the era of globalisation."
Writing in the Sunday Times, Mr Brown said he wanted to "deepen and broaden" Labour's appeal.
"My vision is to build a home-owning, asset-owning democracy, a Britain of ambition and aspiration, where all and not just the few have the chance to own their own homes, buy shares and build up assets," he said.
Tony Woodley, general secretary of the Transport and General Workers' Union, said such policies were "inappropriate" and were leading to privatisation and contracting-out of services in the NHS and government departments.
Mr Hain says the chancellor is "far out in front"
"There is a big question mark over the party's policies and the sooner our party starts to re-engage its activists, the more likely it is that we will win a fourth term," he said.
Dave Prentis, leader of the UK's largest union, Unison, joined other leaders in expressing disappointment in the chancellor's plans for continued reform.
"Just over a year ago he said that there was a limit to the market in the NHS. He now appears to have changed his mind," he said.
"We don't want to go back to the Thatcher days of the market in the NHS, we want to go forward and deliver quality public services."
Derek Simpson, general secretary of Amicus, said the next leader of the Labour Party should follow a "different path" to the current programme.