Tony Blair's powerful farewell speech to the Labour conference has won him breathing space to decide his own departure date, one of the men tipped as a possible successor said today.

Alan Johnson, the Education Secretary, said that the Prime Minister had killed dissent over the timing of his removal from No 10 and would now be staying for some time.

Mr Blair had said he would go within a year but his critics had wanted him to go before next May's local and national elections. Some of Mr Blair's supporters believe he will now go on until the summer.

However, the leadership's renewed confidence took a knock when angry delegates supported a union motion condemning Mr Blair's flagship plans to reform the National Health Service.

The public sector union Unison, which introduced the motion, warned the Government that it risked losing the next general election if it failed to listen to people's concerns about privatisation of the NHS.

It followed an earlier government defeat when delegates called for more direct investment in council housing.

Mr Johnson, speaking on BBC Radio 4's Today programme, said: "If the PM says ‘I want to use the rest of my time to try and resolve the Middle East problem in the same way as we tried to tackle the Northern Ireland problem’, I think it suggests he’s not talking about a couple of weeks - it’s a big problem."

Mr Johnson said he believed the pressure on Mr Blair over when he would surrender the leadership had now effectively been stopped.

"It’s dead in the sense of people seeking to push Tony into a date. He’s said he will not be here, and we know it’s his last conference so we know that sets out a timescale. I really think people now are saying ‘Tony, the date you set down is a matter for you’. It would be crazy to name a date."

Mr Johnson has said he will stand for the deputy leadership but some view him as a challenger to Gordon Brown.

He flatly denied reports that he had already set up a campaign team which was preparing for battle with the Chancellor over the top job. "No. There’s not a team in place," he said. "There’s not a campaign team in place for anything, not deputy leader or leader. There’s no team in place."

The Education Secretary said that the Prime Minister’s much-praised speech to the conference in Manchester yesterday had not been a "farewell concert".

"Old blue eyes will be back - he’s got gigs in Downing Street and in the Palace of Westminster, and a very important agenda that he set out yesterday about pursuing peace in the Middle East," he said.

The former Downing Street aide Jon Cruddas added his name to the list of men and women who want to replace John Prescott as deputy leader.

The left-of-centre backbencher warned that Labour had "lost its way" and said that it was time to "rebuild our party from the bottom up".

Mr Cruddas joins Peter Hain, the Northern Ireland Secretary, and Harriet Harman, the Constitutional Affairs Minister, as declared contenders for the deputy leadership. Mr Johnson and Jack Straw, the Leader of the House, have also expressed an interest but have not formally launched a bid.

Mr Prescott has not yet announced any plans to leave the post he has occupied since 1994, but is widely expected to quit when Mr Blair stands down

Later new Labour came under fire when delegates backed a hard-hitting union motion demanding a rethink of the Government’s "headlong rush" towards a competitive NHS.

The vote came as hundreds of workers at the health service supplies agency NHS Logistics embarked on their second one-day strike over the outsourcing of their jobs to the German-owned private firm DHL.

The NHS vote reflects the scale of unease among unions and grassroots Labour activists over the nature of the reforms, which have seen some GP services, as well as the NHS Logistics operation contracted out to private firms, along with the creation of independent treatment centres and the introduction of the "payment-by-results" system.

The motion from public sector union, Unison, warned that "immense damage" is being done to some local health services because of the massive deficits run up by NHS Trusts struggling to balance their books due to the move to a "competitive, market-based system"

Dave Prentis, Unison general secretary, said the move was about "a moral compass that says enough is enough". When he ran out of time to complete his speech, Mr Prentis's microphone was switched off - prompting angry heckles from the conference floor.

Patricia Hewitt, the Health Secretary, acknowledged there were limits to the role of markets in the NHS.

But she said she was not prepared to turn her back on £1 billion of savings which would be ploughed straight back into frontline services.

After the vote Mr Prentis warned ministers: "If they don’t listen we will lose the next election.

"We have got to stop this arrogant approach from the top that they know what is best. We want to talk to the Government about the real concerns of the Labour party members who have seen in their local areas, ward closures and job cuts."

Labour’s leadership faced another defeat for the second year in succession in a vote calling for cash for new council houses. The result of a card vote taken yesterday produced victory for a rebel motion calling for "direct investment to council housing as a matter of urgency".

Times Recommends

• Charles blazes trail as sun king
• Thalidomiders win payout 50 years on
• Libel gag on talk of 'medical hurricane'