Whitehall’s most senior mandarins have been asked by the Treasury to draw up details of how an extra £25bn-£30bn in public spending cuts could be imposed a year after the next general election, according to cabinet insiders.

The cuts being sought from permanent secretaries would cover the two years after the existing agreed spending review period comes to an end in April 2016, and so would cover the financial years 2016-17 and 2017-18.

It had been known spending cuts of this order would be required in the two years as part of the Treasury deficit-reduction plan, but it had not been known that the Treasury was already seeking detailed examples of proposed cuts. An indication of government thinking is expected in the autumn statement on 3 December.

Some cabinet ministers are aghast that plans are being drawn up privately for cuts going so deep into the next parliament and believe a public debate should be under way now rather than make plans in private before the election. “We need a public debate around all this, and not for this to be decided in a private conversation between the treasury and the civil service,” a source said.

One is understood to have told his permanent secretary not to cooperate with the exercise that started in the late summer, partly because they think the scale of the cuts being planned is not justified.

The cabinet minister acknowledged that senior civil servants have their own careers to consider so it may be that the work is going on anyway without the agreement of elected ministers on the basis that it forms part of the contingency planning and horizon scanning process that applies after the election. The source added that David Cameron was being deeply misleading about the scale of the cuts needed in the next parliament.

The cuts being planned for the second parliament are likely to be tougher to sell politically partly because the public is not as prepared as in 2010 in the aftermath of the global financial crisis. Tax receipts are also lower than had been anticipated, partly because of changes in the labour market, such as an increase in the number of young people in low-paid employment and in the numbers of self-employed.

A commitment by Cameron to protect spending on the NHS from cuts would mean that the impact will be felt more severely elsewhere. Cuts will again squeeze the police, the Ministry of Defence, legal aid and the business department including further education funding, student maintenance loans and science research.

One source said: “The planned cuts would have a massive impact on departments. You could see the Department of Communities and Local Government facing eventual cuts since 2010 of 80%.” The source added that this would have a devastating impact on the housing budget and on local council services.

George Osborne, the chancellor, has vowed to run an absolute surplus in the public finances by 2018-19 and may want detailed ammunition on how cuts could be made so he can control the baseline in any election debate about tax and spending.

An analysis on Monday suggested that spending cuts in the next parliament would be deeper than expected. The Financial Times said cuts would be closer to £48bn between 2014-15 and 2018-19 rather than the £25bn mentioned by Cameron, partly because the prime minister had excluded cuts required in 2014-15 and 2018-19.

The consequence is the combined annual budget of non-protected departments such as local government and defence will come down by a third in real terms from £144bn in 2014-15 to £96bn in 2018-19. Osborne has said he could reduce these cuts by as much as £12bn if he can find cuts to working-age welfare.

Nick Clegg, speaking at the CBI conference in Birmingham yesterday, hinted at the fragile state of the public finances by saying “the nascent recovery is at a very delicate stage”. But the deputy prime minister said he differed from the Tories who want to complete the deficit reduction by the 2017-18 timetable through spending cuts alone. This plan was “neither economically sensible and socially sustainable”. He added: “It would lead in my view to very, very deep cuts in policing, in the business department and in social care. It would also penalise the working-age poor”.