Senior cabinet ministers are privately discussing a plan to scrap the Government's £5bn identity cards programme as part of cuts to public spending, The Independent has learnt.

The ministers believe that some "sacred cows" will have to be sacrificed in the effort to reduce Britain's debt mountain. They are raising fresh questions over the future of the ID card programme as the Cabinet faces renewed pressure to find economies beyond a promised £9bn in "efficiency savings".

"My sense is that ID cards will not go ahead," a senior Cabinet Minister said. "We have to find savings somewhere, and it would be better to shelve schemes like this that aren't popular."

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A ComRes poll for The Independent today finds 55 per cent of voters favour public spending cuts to reduce Britain's debts, against 38 per cent who want taxes to be increased. It also finds that the Tory lead over Labour has widened from 12 to 19 points since the Budget.

Issuing ID cards will cost more than £5bn over the next decade while scrapping the scheme now would leave the taxpayer with a relatively small compensation bill to pay.

Cabinet sceptics are preparing to use the public spending crunch to push for the scheme to be abandoned before the first cards are issued to British nationals this winter.

David Cameron, the Conservative leader, has said the programme will be scrapped if his party wins the election expected to take place in May 2010.

But Gordon Brown has so far proved immovable on the issue, with Jacqui Smith, the Home Secretary, insisting last month that the Government was "on track" to introduce ID cards.

However, there is a growing recognition among ministers that after Alistair Darling, the Chancellor, signalled severe spending cuts in the Budget, some "big ticket" projects will have to be scrapped to help reduce the national deficit. The Home Office is widely considered to be particularly vulnerable to cuts.

Stephen Byers, the Blairite former cabinet minister, has become the first senior Labour figure to acknowledge that ID cards may have to be shelved. He also suggested the expensive planned replacement of the Trident nuclear missile system be abandoned.

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ID cards were championed by Tony Blair and by David Blunkett when he was the Home Secretary.

Mr Brown was initially hostile to the scheme because of its cost but he became an enthusiastic convert, arguing that it would tackle terrorism, organised crime, illegal immigration and identity fraud.

The first ID cards for British citizens will be issued to some airport workers by the end of the year. A widespread roll-out of the scheme is scheduled to begin in 2011. Foreign nationals have already received the first cards.

The Home Office puts the cost of introducing ID cards for Britons at £4.7bn over the next decade and the additional cost of introducing them for foreign nationals at £326m.

There would be a further unspecified cost to Whitehall departments for accessing the biometric database that will underpin the cards. The Government has just signed contracts worth £750m to set up the scheme, one to upgrade passport application systems and the other to set up the database. The contract for the ID cards themselves will be awarded later this year.

Ms Smith has told MPs that cancelling the contracts would cost the Government "in the region of £40m in the early years".

The £25bn replacement for Trident is the most high-profile major Government project that is at risk, but the cabinet source predicted that it would be saved because of the impact that its cancellation would have on jobs, principally at Barrow-in-Furness, where the submarines are built.

The Trident replacement was designed for the Cold War to penetrate well-defended targets in the Soviet Union or China, and opponents say it has been made obsolete by the new threat of nuclear attack from rogue states lacking sophisticated defences.

"There is a case for shelving Trident Two, but the number of jobs that go with it is just too great," said the Cabinet source. "I just can't see us cancelling a Trident replacement now."

Vince Cable, the Liberal Democrats Treasury spokesman, said last week that he believed ID cards and Trident were "sacred cows" that would have to go as part of cuts in public spending.