Britain's nuclear weapons are irrelevant to any existing and foreseeable threats posed by foreign states and there is an urgent need for a wider and more informed public and parliamentary debate about their use, according to an authoritative independent report to be published on Tuesday .

There must be a much deeper debate about whether to retain or modernise the Trident nuclear ballistic missile fleet given its expense – estimated to be be £100bn over its lifetime – at a time of austerity, and the risks of accident and proliferationit creates, it adds.

"Britain's nuclear weapons should be subject to the same cost-effectiveness test and public scrutiny that all public expenditure has to be subjected to," says the report by the Nuclear Education Trust, an independent charity.

Its report, drawn up after consulting a wide range of defence experts, including former defence secretaries and military chiefs, questions the legality of the government's plans to replace the existing Trident submarine fleet given Britain's nuclear non-proliferation treaty obligations. And it says that nuclear weapons, which were not scrutinised in the last Strategic Defence and Security Review in 2010, must be included in the next review due after the general election in 2015.

"Nuclear weapons represent a twentieth-century failure: they are the cold war's unfinished business which should be solved by this generation," says the report. It urges the government to attend an international conference in Mexico later this month on the humantiarian impact of nuclear weapons.

The trust's report coincides with a separate study by Scientists for Global Responsibility (SGR), a British advocacy group, which revealed on Monday that UK government spending on research and development for nuclear weapons amounts to more than £320m a year.

The estimate includes R&D spending on nuclear warheads at the Atomic Weapons Establishment in Aldemaston and development work for a Trident "successor" fleet. The estimate is based partly on data obtained using freedom of information requests.

The R&D spending for nuclear weapons systems is higher than that for any conventional weapons systems during this period and than key areas of UK public spending on civilian R&D.

Dr Stuart Parkinson, the executive director of SGR, said: "These figures show that the UK government's R&D priorities are distinctly warped. I cannot see how they can justify such high spending on developing new ways to deliver weapons of mass destruction, while areas as valuable as renewable energy development receive so much less public funding."

Those consulted by the Nuclear Education Trust, including Admiral Lord West, a former first sea lord, and General Sir Mike Jackson, former head of the army, back a new Trident system despite its cost. Others question its value. "For current threats there is no relevance. But for future threats? Well, it is the 'mere uncertainty' argument," said Professor Michael Clarke, director general of the Royal United Services Institute.

He added: "It's utterly fallacious – if you told the chancellor of the exchequer that the Treasury should fund 20 hospitals just in case there was a pandemic he would laugh at you. Why should this argument be any more credible when it comes to nuclear weapons?"

Madeline Held, the chair of the Nuclear Education Trust, said: "Despite the wide range of contributors, there was a remarkable consensus on many issues: that the UK's defence policy and procurement decisions should be more rigorously evidence-based, that the raison d'être of nuclear weapons has decreased since the end of the cold war, and that progress on international nuclear disarmament is a necessary and desirable goal for which there are concrete opportunities for success."