The business secretary, Vince Cable, has torn into the Conservatives for promising £7bn of new tax cuts at a time of renewed uncertainty about the global economy, saying it was “total fantasy” to think they could be delivered without raising other taxes or making massive extra cuts to public services.

Cable told the Observer that officials inside the Treasury were increasingly concerned that the pledges made by the chancellor, George Osborne, and David Cameron at the Tory conference in October were not affordable and could put the government’s reputation for fiscal credibility at risk.

“When you look at the numbers, tax cuts on any significant scale are simply not deliverable unless you make horrific cuts to key public services such as the police and defence,” Cable said. “Technically, of course, you can always make tax cuts, but if you are to avoid hitting services you would have to put up other taxes or cut services massively. It is total fantasy to suggest otherwise.”

He added: “George Osborne risks undermining his fiscal credibility by promising unfunded tax cuts while at the same time saying he will run a budget surplus.”

Cameron and Osborne are under mounting pressure to explain how their plans for the next parliament will be funded in the autumn statement on 3 December, and how they can be justified at a time when they are also warning about the health of the global economy and its possible effects on UK growth. One option, that would be highly controversial, is for the chancellor to announce further cuts to in-work benefits – a move that would leave the Tories more exposed to claims they are helping the better off at the expense of the poor.

The Tories have said that their pledge to raise the personal allowance – the amount that can be earned before becoming liable for income tax – from £10,500 today to £12,500 by 2020 will cost £6bn, while lifting the 40p tax threshold to £50,000 by 2020 would cost another £1.2bn.

Last week Cameron warned that “red warning lights are flashing on the dashboard of the global economy” in the same way as when the financial crash brought the world to its knees six years ago. Writing in the Guardian, the prime minister said there was now “a dangerous backdrop of instability and uncertainty” that presented a real risk to the UK recovery, and added that a slowdown in the eurozone was already affecting British exports and manufacturing.

New concerns were raised last week about the pace of deficit reduction when the Office for National Statistics released data showing that over the first seven months of the financial tax year, from April to October, the government borrowed £64.1bn – £3.7bn more than during the same period last year – due to disappointing tax receipts and higher than expected spending.

Cable said that while the Liberal Democrats, who have championed the policy of raising the tax-free threshold, remained wedded to it to help low earners, further rises could only be made when they were affordable. The Lib Dems would pay for raising the threshold through a mansion tax and other measures.

An Observer/Opinium poll shows that a majority of people disbelieve the Tories’ pledges on further tax cuts. Of all likely voters, 58% said they thought the government that took power in 2015 would not be able to afford to cut taxes for working people. This included most Conservative supporters (52%), with 39% of Conservative backers saying they believed cuts would be affordable. Some 51% of Labour voters thought cuts would not be affordable, against 31% who said they would be.

Leading economists and commentators have also raised doubts about the affordability of tax cuts, unless accompanied by savage reductions in spending or parallel tax rises. Gavin Kelly, chief executive of the Resolution Foundation thinktank, said: “Everyone knows the next parliament is looking incredibly tough. Over and above all of the cuts in this parliament and the £8.5bn planned for the year after the election, under current plans there is still another £37bn of fiscal pain to come after that. And this is assuming that the OBR’s forecasts for the recovery in tax revenues prove correct. At the moment that is looking increasingly shaky as the low-wage recovery has meant that tax revenues have recently disappointed the Treasury. This is an incredibly difficult context against which to be talking about any significant tax cuts or indeed spending rises.

“Something is going to have to give. Either the boundaries of the state are going to be very significantly redrawn in a way that no party has yet been transparent about, or there will be new tax rises we don’t yet know about, or there will be a slower path of deficit reduction – or a mix of all three. Less than six months out from the election no party has really made clear which it’s going to be.”

Shortly after the Tory conference in Birmingham, Cameron indicated that the tax cuts could be introduced early in the next parliament.

Labour is also pressing the chancellor to explain how the tax cuts would be paid for, and to rule out a rise in VAT, which the Conservatives have refused to do. Chris Leslie, the shadow chief secretary to the Treasury, said he had written to the chancellor several weeks ago but had not received a reply. “I am waiting by my post box,” he said.