Prime Minister Tony Blair has refused to bow to calls for him to promise MPs a House of Commons vote on replacing Britain's nuclear weapons system.
Mr Blair has announced the timetable for deciding on Trident
Mr Blair told MPs a decision on replacing Trident would be taken later this year, saying he favoured the move.
Asked repeatedly whether MPs would get a vote, he said there would be the "fullest debate" but the way to consult people had yet to be decided.
David Cameron said Mr Blair was at odds with Gordon Brown on the vote issue.
Mr Brown signalled in a speech last week that he wanted to replace Trident, which is expected to become obsolete in about 2024.
Defence and aid?
Speaking after the Commons clash, the chancellor responded to criticisms from church leaders in Scotland that funding new nuclear weapons was at odds with his commitment to overseas aid.
"I think what people do know is that we've managed to ensure the defence and security of this country, in a world where we are prey unfortunately, to terrorist threats," he told BBC News.
"At the same time, we've managed to show that we can double overseas aid, we can increase investment in Africa three-fold, we can create a vaccination facility that will ensure that five million children live rather then die.
"I think we've proved that what governments have got to do, you must have defence and security in the modern age and you must be able to help those in greatest need. We're doing both."
At prime minister's questions, Mr Cameron said Mr Brown and Education Secretary Alan Johnson both wanted a Commons vote on the issue.
Like Brent, Tony Blair is now "utterly redundant", says Mr Cameron
He told Mr Blair: "You're saying one thing and the chancellor is briefing another.
"Isn't this part of a wider problem. Isn't there a danger that you are just becoming the David Brent (lead character in BBC comedy The Office) of Downing Street - utterly redundant, you are just hanging round the office."
But Mr Blair said the government was concentrating on policies and he challenged Mr Cameron to debate some of his.
He said the Tories had one domestic policy - creating a new British Bill of Rights - and that had been called "xenophobic" by Mr Cameron's democracy adviser, former Chancellor Ken Clarke.
Voicing his support for keeping Britain's nuclear capabilities, Mr Blair said: "It is important that Britain makes sure that we defend our country properly. I believe an independent nuclear deterrent is an essential part of that."
The exchanges come after former Home Secretary Charles Clarke said Mr Blair had lost direction and authority.
And Foreign Secretary Margaret Beckett urged Mr Blair and Gordon Brown to ensure a smooth transition of power.
Pressed to say whether she believed Mr Blair and Mr Brown could carry out the smooth transition the Labour Party wanted, Mrs Beckett replied: "I think they can do that.
"I certainly hope they will do that," she told The Times newspaper.
But she said it was up to the prime minister and the chancellor to decide if the autumn party conference is the time to signal that they are prepared to hand over power.
"What people want is for there to be a process - which there can easily be - which is supportive of the party and advantageous to the party and not the other way round," she said.