Deep fissures are opening up among the coalition's senior defence policymakers over the future of Britain's nuclear deterrent, the Guardian can disclose.

The splits are being exposed as it emerges that senior officials have not drawn up assessments for ministers about alternatives to replacing the existing Trident fleet of nuclear submarines. Despite this, Liam Fox, the defence secretary, insists the fleet must be replaced by a "like for like" system.

At the centre of the dispute is whether Britain should persist with a continuous at-sea deterrent (CASD) – that is, having one nuclear-armed submarine on patrol every day of the year.

Nick Harvey, the Lib Dem armed forces minister and Fox's deputy at the MoD, is now openly challenging the defence secretary's assumptions. "Alternatives didn't seem to have been given detailed or objective assessments," he said. "The debate has been very much yes or no to this single notion of how a credible deterrent can be provided."

He added: "Supporters of this policy come at it in a very single-minded way and anyone who does not agree is [regarded as being] implacably opposed to a deterrent of any kind."

Referring to the agreement to delay a decision on replacing Trident until after the next general election, Harvey said: "We now have a period of time for a mature debate about alternatives and approaches and the necessary work to be commissioned."

Fox and his supporters believe a post-2015 decision would only consider the number of submarines needed for CASD – whether it can be guaranteed by three ships or by four, as at present – and the number of warheads and missiles on each.

Under the terms of the coalition agreement, the Lib Dems can continue arguing for alternative – and cheaper – ways of maintaining and delivering nuclear weapons.

However, Fox appeared to have bounced the Lib Dems into agreeing with the CASD posture when he told the Commons on 1 February: "It is clear from the coalition agreement that we are committed to maintaining a continuous at-sea minimum credible nuclear deterrent that will protect this country from nuclear blackmail and ensure that we make our role apparent in reductions in total nuclear armaments."

The defence secretary is supported by Tory backbenchers and navy chiefs. However, there is growing concern within the MoD and among army commanders about the cost and need for a like-for-like Trident replacement, especially in light of the chancellor's insistence that the capital cost – estimated at £20bn – as well as the running costs should come out of the core defence budget.

Concerns are now spreading to Labour ranks. Lord Browne of Ladyton, defence secretary when the Blair government made its case for replacing Trident in 2007 – when it had to rely on Conservative votes – says he was not presented with sufficient facts and figures about the choices open to the government. He is co-chair of a new cross-party Trident commission sponsored by the British American Security Information Council (Basic), a defence thinktank.

He attacked the government for excluding nuclear weapons from its recent strategic defence review.

Ian Kearns, Basic's research director, said he recently asked a government official what studies had been made into how long it would take and what it would cost to reconstitute the Trident deterrent if it were withdrawn from active deployment. The answer was none. Harvey called the omission "extraordinary".

Lord Guthrie, former chief of defence staff and a member of the new Trident commission, said he wanted to look into the "opportunity costs" of replacing the system.

An MoD spokesman said: "As the prime minister said in the House of Commons last week this Government is committed to maintaining a continuous at sea nuclear deterrent based on Trident".

He added: "Nuclear deterrence policy is, however, one of the issues on which the two Coalition parties have agreed to disagree".