Politicians are competing to prove how parsimonious they are. David Cameron wants to freeze the BBC licence fee to save £68million. Alistair Darling is demanding £5 billion of “efficiency measures” across Whitehall. George Osborne and Ken Clarke are arguing about whether a Tory Government could afford an inheritance tax cut that would cost £3 billion. But the country has debts heading for £2 trillion. It's as if the political class is promising to stop buying Manolo Blahniks when the house is about to be repossessed.

Yet sitting in the attic is a valuable antique - a family heirloom, inherited from another age - that is worth tens of billions of pounds. It's never used and costs a fortune to maintain. How long before Gordon Brown or Mr Cameron proposes that the Trident nuclear missile replacement should be scrapped?

Last week, the Prime Minister tiptoed up to the issue in a speech in which he said that he wanted a world free of nuclear weapons. Naturally, he proposed a “grand global bargain” under which Britain would reduce its number of warheads. But his spokesman insisted that the plan to replace the four Trident submarines themselves would go ahead.

Behind the scenes, however, the Government is taking a long hard stare at the programme. It is estimated that the replacement will cost between £15 billion and £20billion, but with annual upkeep of £1.5 billion, the total over 30 years could rise above £65 billion. That's an awful lot of schools and hospitals. As one minister put it, to get rid of Trident would be a “welcome relief on public spending”.

It won't happen immediately but scrapping Britain's nuclear deterrent is on the cards for the first time since Labour came to power. As the Government's counter-terrorism strategy paper will make clear today, the biggest threat is now from extremist groups rather than enemy states at which missiles can be aimed.

There is widespread recognition in Whitehall that the nature of warfare has changed. John Hutton, the Defence Secretary met Robert Gates, his opposite number in Washington last week and agreed that Britain and America would carry out a joint review of defence strategy in the light of the counter-insurgency operations in Iraq and Afghanistan. Although this will not look at nuclear weapons, it is clear that the Trident submarines are not much of a deterrent to a suicide bomber. It is also harder to argue that Britain's permanent seat on the UN Security Council depends on retaining its weapons when countries such as India and Pakistan have a nuclear capability but no chair.

The truth is that all these arguments have gained saliency because of the recession. The policy of Mutually Assured Destruction seems less appealing when we face financial Armageddon. According to one Foreign Office source: “Trident is not at all useful for most modern warfare... we should move towards [scrapping it] in the medium term.”

Although the official line remains that Britain will retain its nuclear capability, the language in Whitehall has changed. One minister says that Trident is more useful as a “tool for global disarmament than for UK defence”. This means that even if the Government did want to abandon it eventually, it would be wrong, tactically, to announce such a plan yet. “The when and how of playing the card matters,” the minister explains. “Just dumping it gets you nothing. You do it when it will spur maximum disarmament by others.”

According to Baroness Williams of Crosby, the Liberal Democrat peer who advises the Prime Minister on nuclear proliferation, and was praised by him last week, Britain could use its nuclear weapons as a bargaining tool in the runup to the Non-Proliferation Treaty Review conference next spring. “Trident could be a crucial factor in reaching a serious international agreement,” she told me. “But to announce it now would be to chuck your queen away when you've only just started the chess game.”

One option being discussed in Whitehall is to offer to abandon the programme altogether, another is to suggest scaling it back by reducing the number of submarines or commissioning cheaper land-based missiles. A third proposal is to have a joint nuclear deterrent with the French - Europe's other nuclear power - although this is likely to prove too controversial for ministers to accept.

For new Labour, Trident has always symbolised the break with old Labour's CND card-carrying days. For Mr Brown, the nuclear deterrent is proof of his patriotism and commitment to the military - he made a point of announcing that it would be replaced, even with Tony Blair still in No10.

But it is no longer only leftwingers who are sceptical about the programme. Charles Clarke and Michael Portillo have both suggested that Trident is an anachromism. Some in the military Establishment - including Field Marshal Lord Bramall, the former Chief of the Defence Staff - now argue that nuclear weapons are “irrelevant” in the post-Cold War era and say money should be spent on troops and equipment instead. Given that the running costs of the Trident replacement will be between 5 and 6per cent of the Ministry of Defence's annual budget it is likely that at least some serving members of the top brass agree.

In the US, hardened diplomats such as Henry Kissinger and George Schultz have started banging the drum for disarmament. The election of Barack Obama - who has made clear that he would like to reduce America's nuclear capability - has changed the mood music internationally. As one minister puts it: “An argument that was completely off limits, for people in sandals and T-shirts has been brought into the mainstream national security debate.”

The question is, however, will Mr Brown or Mr Cameron be willing to give up the ultimate boy's toy?

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