Theresa May faces a House of Commons revolt over universal credit after the minister responsible for the system contradicted the government line and admitted it will leave some families “worse off”.

The Department for Work and Pensions (DWP) needs to pass regulations in order to implement the next phase of the “managed migration” to the controversial new benefits system, but a growing number of Conservative MPs have publicly expressed their concerns. The changes are meant to affect another 3.95 million people from July.

The government’s task was complicated on Thursday when the work and pensions secretary, Esther McVey, broke with the Downing Street line and conceded some families would lose out under UC, contradicting the prime minister’s remarks earlier this week.

“I’ve said we made tough decisions. Some people will be worse off,” she told the BBC. “Under the old system, 700,000 people didn’t get £285 a month, so they didn’t get the money they were owed. Under the old system the most vulnerable in society weren’t getting as much money as we are now going to give them.”

Labour is urging the government to allow a full debate before the regulations are passed, amid growing dissent about UC, which is significantly less generous than the benefits it is replacing, after deep cuts imposed by George Osborne.

The process will be further complicated by the Democratic Unionist party, whose 10 MPs usually vote to support the government but are in a standoff with May over Brexit, and a handful of Tory rebels, who could be enough to put her majority at risk.

Several Tory MPs, including Plymouth’s Johnny Mercer, the education committee chair, Robert Halfon, and a persistent critic, Heidi Allen, have called for cuts to the system to be reversed.

The former prime minister Sir John Major said on Thursday that the welfare overhaul could be as damaging to the Conservatives as the poll tax was in the 1980s.

One well-connected Tory backbencher said there was a concern the policy could end up being “the final straw” for May’s fortunes, with a number of MPs worried about the rollout of the programme.

“This is especially so in marginal seats – it’s like the poll tax,” the MP said. “It’s a good principle, but the implementation must be generous. If not, there’s a huge risk of a backlash. No one is focusing on it properly because of Brexit.”

A DWP source said the regulations would go before parliament in the autumn.

Downing Street distanced itself from McVey’s comments, insisting she was referring to new claimants who may not be paid as much as they would have been in previous years.

May’s spokeswoman said: “The PM made it really clear that when people move across on to UC as part of managed migration there is not going to be a reduction in their benefits; that’s because we’ve put £3m of transitional protections in.

“At the same time, there are people who are making a new claim or who have had a change in their circumstances and their payment will reflect their new circumstances as you would expect.”

Labour hopes to expose Conservative disquiet about the system in an opposition debate in parliament on UC planned next week.

In a debate last year, Labour inflicted a symbolic defeat on the government hours after the then DWP secretary, David Gauke, was forced to end a 55p-a-minute helpline for welfare claimants because of a Tory backlash.

Mercer tweeted: “Universal credit was designed so that no one would be worse off. “Stop the tax-free allowance rise and reinvest into UC, or I can’t support it. Not politically deliverable in Plymouth I’m afraid.”

Fellow Tory MP Nigel Mills, a member of the work and pensions select committee, said the government should slow down the rollout while there were “widespread concerns about the approach the government is taking”.

While Major said he supported the logic behind the welfare changes, he questioned whether they were workable in practice.

“In order to introduce something like universal credit, you need to look at those people who in the short term are going to lose, and protect them, or you will run into the sort of problems the Conservative party ran into in the late 1980s,” he said.

The former prime minister, who entered Downing Street in November 1990, nine months after rioting broke out in London over Margaret Thatcher’s doomed poll tax reforms, denied he was predicting civil unrest.

“If you have people who face that degree of loss, that is not something the majority of the British population would think of as fair, and if people think you have removed yourself from fairness then you are in deep political trouble.”

The former Labour prime minister Gordon Brown has urged the government to abandon the full national rollout, suggesting Britain was otherwise on course for a summer of discontent.

Speaking in Bristol on Thursday, the Labour leader, Jeremy Corbyn, whose party advocates scrapping the entire policy, said the “experience of universal credit has been that the majority of people are considerably worse off”.

Universal credit’s architect, Iain Duncan Smith, claimed it was working well and that thousands of people would find themselves better off in work, but he admitted there was an issue with the policy as a result of £2bn being taken out by the government in 2016, a move which prompted his resignation from the cabinet.

“We should direct the money back into universal credit exactly as it was originally planned to be rolled out,” he said.