Chancellor under pressure from cabinet to abandon plans to impose a £2bn levy on the region's oil and gas companies

George Osborne, the chancellor, is under pressure from within his cabinet to back down on his unexpected plans to impose a £2bn windfall tax on North Sea oil and gas companies.

Fellow ministers are frustrated that they were given no long-term warning by the Treasury of the plan in advance of the budget and that the oil companies were given no chance to be consulted.

It is also being argued that the sudden change in the tax regime ran counter to a series of pledges Osborne gave to the North Sea oil industry in opposition. He told the Aberdeen Press and Journal in 2009 that one of his earliest budget commitments would be to set up a parliament-long stable tax regime for the oil industry.

The Treasury minister Justine Greening went to a bruising meeting with oil companies attended by other government ministers in which she was told that the industry has lost trust in government promises to maintain a stable tax regime in the North Sea. One witness said she was "grilled alive". At a meeting described as cold and pointed, attended by the Scottish secretary, Michael Moore, and the energy secretary, Chris Huhne, she was told she had put 40,000 jobs at risk.

Greening was told by oil companies including Total and Shell that Statoil was suspending a $10bn (£6.2bn) project at the Bressay and Mariner oil fields – two of the most valuable deposits left in the North Sea – to review whether the investment is still worthwhile.

The oil companies said they were responsible for a quarter of private sector capital investment in the UK, and were quite prepared to pull the plug on a large part of this investment unless the tax regime were changed. They pointed out that as reserves are slowly depleted, companies need better incentives to pump the remaining, harder-to-reach resources.

There were also claims that senior cabinet ministers with a direct involvement in the industry were not informed more than 48 hours before the budget of the plan to make the tax raid on the profits of the oil industry.

Late representations were made in an attempt to introduce some flexibility based on the price of oil, and ministers opposed to the rise are urging the Treasury to raise the price at which the higher tax kicks in.

Supporters of the chancellor claim the principles were discussed between the Treasury chief secretary, Danny Alexander, the deputy prime minister, Nick Clegg, Osborne and David Cameron.

Last Wednesday's budget increased by 12 percentage points the tax levied on North Sea companies, on top of corporation tax, in order to raise £2bn a year to pay for a 1p reduction in the duty on petrol and diesel and scrap a further 5p increase due under plans agreed by the last government.

The oil and gas industry's tax bill for the next financial year is expected to be £13.4bn, compared with £8.8bn this year.

In a sign of the problems developing over the issue, Alexander who represents a Scottish constituency, denied the tax raid had been his idea. "We don't expect this tax change to have a significant effect on production and investment and therefore on jobs in the coming years," he said.

The Scottish National party has already described the oil grab as Alexander's political epitaph, but what will worry him more is the lack of support from key cabinet allies and normally loyal Scottish Liberal Democrat MPs, such as Malcolm Bruce.

Bruce accused Alexander of being "economically illiterate for coming up with a "populist move" that could kill off investment in the North Sea.