Labour aims to put ministers on the spot over the cost of living by forcing a Commons vote on a windfall tax for North Sea energy profits, amid some signs of increasing support for the policy on Conservative benches. Before the vote, to be instigated by an amendment to the Queen’s speech on Tuesday, Labour released calculations that forecast North Sea oil and gas profits for 2022/23 would be greater than all UK households have paid in increased energy bills. The government was “simply running out of excuses” to not impose a one-off levy on profits boosted by high energy prices, money that could be channelled to help with bills, said Ed Miliband, Labour’s shadow energy secretary. While the Labour amendment refocuses attention on an issue proving increasingly uncomfortable for ministers, and the party has had recent success with other parliamentary procedures such as humble address motions, an amendment to the Queen’s speech is highly unlikely to pass. The wider idea of the tax is nonetheless gaining some momentum among Conservatives, with public supporters including Robert Halfon, the senior backbencher who is a leading Tory voice on cost of living issues, and Mel Stride, the former minister who chairs the Commons Treasury committee. Zac Goldsmith, the peer whose ministerial role covers the environment department and Foreign Office, argued that a windfall tax would help both with reaching net-zero targets and cost-of-living pressures. Goldsmith told the Guardian that people “need something they actually feel – directly”, adding: “So many are struggling at the moment.” At least one other junior minister has told colleagues they back the idea. Kwasi Kwarteng, the business secretary, is the most vehement cabinet opponent of a windfall tax. Rishi Sunak, the chancellor, does not support the idea, but has indicated it could be necessary if energy firms do not sufficiently reinvest the additional money. The Labour amendment would add wording saying that MPs “respectfully regret that the Gracious Speech fails to announce a windfall tax on the profits of oil and gas producers, in order to provide much needed relief from energy price increases for households”. Labour’s calculations, based on estimating future North Sea profits based on tax receipts for 2022/23 projected by the Office for Budget Responsibility, suggest that total profits for the year will be £19.5bn, up from £11.75bn the year before. The 2022/23 total is less than the estimated £18.8bn cost to the UK’s 27.8m households of a price cap rise of £680. “It’s time the government dropped their threadbare excuses, did the right thing and put a windfall tax on oil and gas producers to deliver real help for families and pensioners,” Miliband said.