Rishi Sunak is facing a budget backlash from traditional Tories, with five former cabinet ministers warning the scale of spending and taxes would stifle growth.

The chancellor received a lukewarm reception from a string of Conservative grandees after his budget on Wednesday. They put him on notice that they would not put up with a “big state, high tax” situation for long.

Sunak has always pitched himself as a fiscally hawkish Tory whose role model is the Thatcherite chancellor Nigel Lawson. He used the second half of his speech to promise backbenchers: “My goal is to reduce taxes.”

But despite this promise, senior backbenchers have used two days of budget debates in the House of Commons to lay into him over the scale of public spending and taxes, arguing it was not a Conservative way to encourage growth.

Robert Jenrick, who was in the cabinet until the latest reshuffle, said he was “very concerned about the current level of public spending, and the size of the state”.

“The overall tax burden is at its highest sustained level in peacetime, and I worry that we will not be able to go much further than that,” he said.

Theresa May, the former prime minister, also made an intervention to question the prediction of low growth towards the end of the parliament combined with public spending rising at a higher rate.

“I am interested by the fact that the government appear to think that they can sustain a situation wherein public spending increases by, as I think … the chancellor said, 3.8% a year, but the economy grows at less than half that rate,” she said.

She also questioned whether Sunak was fixing the fiscal rules to make sure they never needed to be met.

But the toughest warning to Sunak was delivered by Chris Grayling, the former cabinet minister and fellow Brexiter, who said: “My message to the Treasury is that I – and I am pretty sure an awful lot of people on the Conservative benches – will be holding the chancellor’s feet to the fire to deliver on that, because we cannot plan a future, as Conservatives, as a big-state, high-tax party. We are a small-state, free-enterprise party.”

John Redwood, a former cabinet minister from the Major era, focused his demands on “cuts in tax rates now to promote faster growth”.

“The chancellor rightly says he wants them in due course,” he said. “They should not be a reward for managing to grow against the headwind of high taxes. They should be a necessary part of a growth strategy. They will speed growth and make the rest easier to achieve.”

His comments were backed by David Davis, the former Brexit secretary, who said: “The area where I disagree with the government’s strategy is on the level of income tax, national insurance contributions and taxation generally which, in my view, is likely to raise significantly less money than the Treasury spreadsheet tells them.

“The simple truth is that the increase in [national insurance contributions] will undoubtedly depress growth and employment and, as a result, depress the tax take.”

Despite his hints that he would want to cut tax before the next election, Sunak refused to commit to that in a round of broadcast interviews on Thursday morning, arguing instead that the change in the universal credit taper rate was effectively a tax cut, because it would allow lower paid workers to take home more of their earnings.

Asked on Sky News whether he would cut taxes before the next election, Sunak said: “We started cutting taxes yesterday, our priority being those on the lowest incomes.”

He also defended cutting domestic flight taxes in the run-up to next week’s Cop26 summit, after being accused of going “headlong in the wrong direction” about tackling the climate emergency.

Labour said it was an “astonishing” announcement from the chancellor in Wednesday’s budget, given the UK government will urge many world leaders, set to arrive in Scotland within days, to speed up decarbonisation plans in their own countries.