Conservative MPs told the prime minister that expanding existing support schemes would not be enough to help consumers hit by significant price hikes, as Downing Street ruled out delaying a tax rise this April. The chancellor, Rishi Sunak, said on Thursday that the Treasury was examining ways of mitigating the impact of soaring energy prices on consumers when the price cap is reviewed in February. The effect of the new cap will be felt from April, the same month the 1.25 percentage point rise in national insurance will come in. But a number of senior Tories told the Guardian that measures such as expanding the warm homes discount for vulnerable families would do nothing to help the majority of their constituents – saying mailbags were “filling up” with concerns. MPs have repeated calls for a VAT cut on energy bills and the removal of environmental levies – even if it meant paying for the beneficiaries out of direct taxation. Craig Mackinlay – chair of the Net Zero scrutiny group of Tory MPs who say they are concerned about the cost and effectiveness of the government’s environmental measures – said that would “smoothen the immediate load on people … I think that would be a better system, perhaps only temporarily until we get more stability in the international energy market.” Robert Halfon, chair of the education select committee, said there should be other tax cuts for the lower paid to ease the burden, including minimising green levies when energy prices rise. “I’m not a climate denier, I believe we need to act,” he said. “But we have a cost of living crisis at the moment – people in my constituency are struggling to feed their families, only just making ends meet but not eligible for these other schemes.” MPs have said privately that Boris Johnson could face serious rebellions into the spring as they signal their discontent. “It will be a big one – this is bread and butter politics,” said one MP. “Why would people vote Conservative if they can’t feed and clothe their families? Labour are not stupid, they talk about it week after week.” Johnson’s spokesperson said there were no plans to delay the 1.25 percentage point rise in national insurance, which is expected to raise £12bn. Jacob Rees-Mogg, the House of Commons leader, is understood to have asked Sunak during Wednesday’s cabinet meeting to reconsider the increase. “I think it’s important not to lose sight of what the national insurance measure seeks to achieve,” the spokesperson said. “We know that one of the public’s main priorities … is the backlog in our NHS. That’s their priority and that’s what we will deliver on. “In the longer term, it will also tackle another fundamental issue left aside for too long, which is the unfairness in our current social care system. “Those are two key priorities that need to be funded. We’re doing that in a fair and progressive way. And that’s why we are taking this approach.” The Treasury is understood to be examining targeted measures to help vulnerable consumers with higher bills, such as extending the warm homes discount, but Sunak is thought to be sceptical of cutting VAT. Speaking at a vaccination centre in Haywards Heath, the chancellor said there were a number of measures already in place. “Of course I understand people’s anxiety and concern about energy bills in particular,” he said. “Of course we’re always listening, making sure the policy we’ve got will support people in the way we want it to, and that’s what our track record over the last year or two shows.” For example, he said, the government had increased the national living wage in the spring and reduced the universal credit taper rate, as well as helped towards bills for pensioners and vulnerable families. But Rees-Mogg’s intervention is likely to reignite debate in the party over the national insurance rise. Before Christmas, Lord Frost resigned from the cabinet citing high taxation, as well as Covid policy. The transport secretary, Grant Shapps, said the tax decision had been taken and would go ahead. “We’ve made our decisions. We have a collective responsibility,” he told BBC Radio 4’s Today programme. During questions in the Commons, the shadow Commons leader, Thangam Debbonaire, teased Rees-Mogg about his intervention, saying scrapping the tax was “something we have been calling for since it was announced … I wonder – is he about to cross the floor?” Rees-Mogg did not respond directly but said Labour’s call to end VAT on fuel was only possible because of Brexit. “If we were still in the megalithic state that she used to so campaign for … we would not be able to cut VAT on fuel.”