Philip Hammond has told his defence ministers to privately lobby the shipbuilding unions because of concern within government that Labour MPs are turning against Ed Miliband's decision to back plans to replace the Trident nuclear deterrent.

According to a number of Westminster sources, the defence secretary decided to make the unusual move after junior ministers warned him that parliamentary support for the £80bn Trident renewal was beginning to ebb, particularly on the Labour backbenches.

Senior Tory MPs have recently voiced doubts about the wisdom of replacing Trident and the Liberal Democrats are committed to finding alternatives.

Defence officials confirmed that Hammond told his junior ministers, including Mark Francois and Lord Astor, that they needed to lobby Labour's union supporters within the shipbuilding industry to stop the party going soft on the issue.

"The Tories don't want Labour having a wobble on this," said one Whitehall source. "Hammond clearly doesn't like what he has been hearing."

Another source added: "Ed Miliband would be insane to reopen the Trident debate before the election. But everyone knows there are a number of MPs in his party who are not behind him on this."

Labour said Hammond should "keep his nose" out of the party's affairs.

"He would be better off spending his time trying to sort out of the mess he has made of the Ministry of Defence. Ed Miliband has made clear his commitment to replacing Trident."

Neither of the main parties wants Trident to become an issue at the next general election, but the huge cost of building four new submarines to provide "continuous at sea deterrence" has led senior MPs across Westminster to question whether the country can afford such a commitment at a time of continued austerity.

The money for the successor submarines will come out of the already stretched MoD budget, which is still under huge pressure, despite tens of thousands of civilian and military redundancies.

The Tories were shaken when James Arbuthnot, their former defence minister, who is now chair of the defence select committee, revealed that recent cuts had encouraged him to speak out about his own doubts about Trident renewal. "Nuclear deterrence does not provide the certainty that it seemed to in the past. It's not an insurance policy, it is a potential booby trap," he said.

Hammond was warned that the mood in Labour was also divided and that some in the party were calling on the leadership to adopt a more neutral stance.

There have also been rumours sweeping Westminster – denied by Labour – that members of the shadow cabinet have been pushing for a change in posture.

Hammond suggested intense lobbying of the Keep our Future Afloat group, which campaigns for the future of ship and submarine building at Barrow-in-Furness, in Cumbria.

The group is part-funded by the Confederation of Shipbuilding and Engineering Unions. This alliance includes Unite, which is Labour's largest donor, having raised almost £800,000 in the three months to last September, and the GMB, the third largest union affiliated to Labour and the donor of more than £600,000 in the same period.

Though the final decision on Trident renewal does not have to be taken until 2016, a sum of £3bn has already been set aside for preliminary procurement and designs, and David Cameron has insisted that replacing Trident is a defence priority.

That view is increasingly being challenged by MPs and peers, including the former Labour defence secretary, Des Browne, who was in charge at the MoD when Tony Blair's government committed to replacing Trident eight years ago.

"Parliamentarians from all parties and in both Houses are much more questioning about the arguments that underpin like-for-like renewal than previously," Lord Browne said. "Consequently, in an age of austerity where public spending is reducing, they are much more sceptical than previous generations. If anything, I am surprised that it has taken ministers until now to wake up to this change. Fewer politicians accept the arguments for continuous at sea deterrence without question than ever did before."

Browne said the UK needed to have "a proper strategy, a glide path" to reduce reliance on the nuclear deterrent.

He added: "For about three years I've been speaking openly and publicly that I am no longer prepared to accept the old arguments that justified keeping submarines at sea continuously – particularly that we have to do this otherwise we'll forget how to do it. That is hardly persuasive."

A spokesman for Keep our Future Afloat said it was surprising that Hammond took this approach. "We have had assurances from Labour that they are committed to replacing Trident."

A Conservative source said: "Renewing our continuous at sea nuclear deterrence is in Britain's national interest. We are happy to work with any other party who shares our belief that a like-for-like replacement of our Trident armed submarines is the only way of guaranteeing our security.

"We are confident that Labour is committed to replacing the deterrent, and the government is pressing ahead to ensure Britain has the ultimate security guarantee, unlike the Liberal Democrats who want some part-time deterrent with dummy missiles, providing Britain with no security."

A Labour spokesman insisted there had been no change in the party's position and that the shadow defence secretary, Vernon Coaker, was strongly committed to replacing Trident.

Last week, the Royal United Services Institute thinktank suggested Britain could save billions of pounds if it cut the Trident nuclear submarine fleet from four to three.

In a 24-page report, the research analyst Hugh Chalmers argued that Britain could maintain a credible deterrent with just three submarines.

"It is not immediately apparent if Russia, China or, indeed, any other state would feel any less threatened by the UK's nuclear forces were they occasionally unavailable," he said.

Arbuthnot said his certainty about the need to replace Trident had been ebbing away. "With the defence budget shrinking, you have to wonder whether [replacing Trident] is an appropriate use of very scarce defence sources. You have to wonder whether nuclear deterrence is still as effective a concept as it used to be in the cold war."