A clear majority among the general public and leading opinion-formers wants a cheaper alternative to Britain’s nuclear deterrent, either by reducing the number of submarines in the system or scrapping it altogether.

The findings, contained in a YouGov poll commissioned by Chatham House, the think-tank, come as the government prepares to announce whether it will press ahead with plans to spend £20bn building a new submarine platform for the deterrent.

Liam Fox, defence secretary, has said the government’s Strategic Defence and Security Review, to be concluded this autumn, will look at expenditure on the Trident system. But he has already said the new deterrent, to be built by 2024, will be submarine-based. He has also strongly indicated Britain will not reduce the number of submarines in the system from four to three, as mooted.

However, YouGov’s poll of some 900 “elite” opinion formers – from business, Whitehall, the media and the voluntary sector – and nearly 2,500 members of the general public, conducted at the end of June, indicates the pressure government is under to make savings.

Some 50 per cent of members of the public said they either wanted a cheaper system or for the deterrent to be scrapped. Some 29 per cent favoured a “broadly comparable” replacement.

Among the opinion formers, opposition to a like-for-like replacement was even stronger. Some 72 per cent said they wanted a cheaper deterrent or for Britain to scrap nuclear weapons altogether. Only 22 per cent backed like-for-like replacement of Trident.

On Afghanistan, the poll found a clear rejection of David Cameron’s policy of keeping British troops in the country for up to four or five more years.

The poll found 77 per cent of the public thought troops should be brought home immediately or that a timetable should be set to withdraw them “within the next year or two”. Only 17 per cent said Britain should keep troops in the country “as long as they are needed”.

Among opinion formers, 70 per cent said Britain should bring troops home immediately or within two years. Some 26 per cent said they should be kept in Afghanistan as long as needed.

One of the main findings of the poll is the sharp divergence between the general public and the opinion formers over what Britain’s future global role should be.

Some 62 per cent of the public agreed that Britain “should seek to remain a great power, with substantial armed forces and our own seat at the United Nations Security Council”. Only 22 per cent backed the statement that Britain “should accept that it is no longer a great power, cut its defence budget accordingly and give up the UN seat”.