David Cameron is to delay holding a parliamentary vote on renewing the Trident nuclear weapons programme until after a referendum on Britain’s EU membership, according to senior Whitehall sources.

The prime minister believes that the referendum campaign, which could be in full swing in just over a week’s time, will complicate efforts to build a strong national consensus over the £31bn renewal of the nuclear deterrent.

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There had been an expectation that the “maingate” vote to approve the Successor generation of four nuclear submarines would be held in March. But it will be delayed until at least July if the EU referendum is held on the prime minister’s preferred date of 23 June.

The decision to delay the vote will fuel speculation that Downing Street is seeking to exploit Labour divisions over the nuclear weapons programme.

Cameron insists that his focus is on making and winning the argument for renewing the Trident programme. But he believes that Labour’s confused position is helping his campaign to reach out to middle ground voters.

He mocked the shadow defence secretary, Emily Thornberry, in the House of Commons on Wednesday for adopting “another completely ludicrous Labour position on defence”. Thornberry, a Trident sceptic who is conducting a review into Labour’s support for the programme, said the submarines could be as outdated as Spitfires within the next decade because China and Russia may be able to detect them.

Jeremy Corbyn, who has been a member of the Campaign for Nuclear Disarmament since 1966, wants to abandon Labour’s support for multilateral disarmament in favour of unilateral disarmament. But he faces strong resistance from trade union leaders and may struggle to change the policy at the Labour conference in the autumn.

If the EU referendum is delayed until September – a possible scenario if Cameron fails to reach agreement in his renegotiations next week – there is an outside chance that the parliamentary vote could still be held in July.

The government acknowledges that it faces a particular challenge in arguing in favour of the renewal of Trident: the threat from other nuclear-armed states. Five countries – Russia, Iran, China, North Korea and Pakistan – are seen to present varying degrees of threat over the next 50 years.

Iran presents no threat at the moment in the wake of its nuclear deal, but there is a belief that the deal offers no guarantee over the coming decades.

Pakistan is not seen to represent any danger to the UK, although there are fears that it has the capability and the will to launch an attack as the smaller of the two nuclear powers on the Indian subcontinent.

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North Korea is seen as deeply unstable and a threat as it embarks on missile tests, but the two most worrying big powers are Russia, which is testing Nato defences on a regular basis, and China. Beijing enjoys more friendly relations with Nato countries than Moscow but, in every war game carried out by Washington, the US ends up in a conflict with China.

MPs will be voting on the entire Trident replacement programme which, if approved, will see the first of four Successor submarines come into service in the early 2030s at an overall cost of £31bn. There is also a further £10bn in contingency earmarked.

The government is opting for four submarines to guarantee the so-called “continuous at sea deterrent” which means that at least one nuclear armed submarine is on patrol at any one time. Under the programme, a second submarine is on standby at the Faslane base on the river Clyde in Scotland, while a third one undergoes repairs and a fourth has a full refit.

While the vote is designed to give approval for the entire programme, the actual procurement will take place on a rolling basis every three years. The government believes that previous defence projects show that lumping a major procurement into one contract can lead to huge extra costs. Contractors then add in extra costs to insure against overruns.

The government is confident that the Trident renewal will be kept within budget because 60% of the design of the new submarines has already been completed. At this stage of the programme for the Astute class of submarines, only 15% of the design had been completed.