Conservative backbenchers, including the former work and pensions secretary Iain Duncan Smith, are preparing to campaign against £3bn of planned cuts to in-work benefits, in a fresh sign of the pressure Theresa May faces from within her own party.

Veterans of the backlash against the deep cuts to tax credits George Osborne was forced to withdraw last year are gearing up to put pressure on his successor, Philip Hammond, in the run-up to November’s autumn statement.

They would like the chancellor, who has said he will “reset” tax and spending policy in the wake of the Brexit vote, to ease the hardship of families who are set to receive significantly lower handouts under the new universal credit (UC) system.

Heidi Allen, the South Cambridgeshire MP who confronted Theresa May about the issue at Wednesday’s prime minister’s questions, told the Guardian: “MPs, lobby groups – we’re all girding ourselves for a campaign on this, and I won’t rest until I have tried my damnedest to get this at least softened.”

She pointed out that the cuts will bite gradually, as UC is undergoing a staged rollout to households across the country. “I just think this is a ticking time bomb,” she said.

The prime minister has already faced vocal criticism from shifting groups of her own MPs on a series of issues, including grammar schools and parliamentary scrutiny of the Brexit process, and has opted to postpone a vote on airport expansion to see off the threat of resignations.

Heidi Allen MP.

While there is no parliamentary vote planned on the cuts, which have already been legislated for, the spectacle of centrist Tories taking to the airwaves to accuse the government of failing to protect the poorest families will underline the challenge May faces in governing her own party.

Conservative MPs are particularly concerned about the low earnings thresholds workers hit before they start to lose some of their benefits; and the steep withdrawal rates, which mean some groups of workers would keep just 24p of every extra pound earned under the new system.

David Burrowes, the Enfield Southgate MP who supported the battle against the tax credit cuts, said: “I share the concern that the changes to work allowances will mean that we do not yet have a welfare system where work always pays and too many people will be in work but in poverty.”

Allies of Duncan Smith say the former cabinet minister is preparing to voice his own concerns about the UC cuts, amid fears that the system, which he championed in government, is now not generous enough to give low-paid employees an incentive to take up more work.

His former aide Philippa Stroud has said she would like to see the planned increase in the tax-free personal allowance cancelled, and the money saved used to make UC more generous.

Analysis by the Resolution Foundation thinktank suggests that families would be £1,000 a year poorer under UC, if the cuts are implemented.

“Many MPs thought the tax credit cuts row had ended with the previous chancellor’s U-turn last year. But the £3bn cuts to universal credit that will be rolled out over the parliament could prove just as controversial,” said Resolution’s senior economist, David Finch.

He said reversing the cuts would show May was genuinely concerned about households that are “just managing”, as she suggested in her first speech in Downing Street.

“A move by the chancellor in the autumn statement to reverse the planned cuts to work allowances would send a strong message that the government’s welcome rhetoric is being backed by bold policy decisions.”

The Lib Dem leader, Tim Farron, said: “Theresa May and Philip Hammond have as much contempt for low income families as David Cameron and George Osborne ever did. If they really cared about helping everyone in our economy they wouldn’t be ploughing on with George Osborne’s universal credit cuts that will hit over 2 million low-income working families.”

Damian Green, the work and pensions secretary, has made clear he has no plans to seek fresh savings from the welfare budget, but Whitehall sources insisted the cuts that have already been budgeted and legislated for will go ahead.

A DWP spokesperson said: “There are no plans to revisit the work allowance changes announced in the budget last year. As our secretary of state has previously made clear, there are no further welfare savings planned in this parliament.”