Leaders of two of the biggest unions have added further pressure on the government over its plan to cut winter fuel payments for millions of pensioners in England and Wales.

Unite and the Public and Commercial Services Union have criticised the plan, while the head of the Trades Union Congress which brings together the unions also expressed his concerns.

It comes as the prime minister faces a potential rebellion at a vote in the Commons on Tuesday if Labour MPs refuse to support the policy.

Prime Minister Sir Keir Starmer has said the cut is necessary due to the state of the country’s finances.

The change will mean more than 10 million pensioners will no longer receive the payments of between £200 and £300 a year, which will now only be made to those on low incomes who receive certain benefits. Charities and many MPs are concerned about those still on a relatively small income who will miss out.

Unite general secretary Sharon Graham told the BBC the government needed to be ”big enough and brave enough” to admit they have made a mistake.

Speaking from the TUC’s annual conference in Brighton, she said: “We think it’s wrong that the government has made a choice to cut the winter fuel allowance.”

She suggested that the new government was, by contrast, “leaving the very rich and wealthy untouched” and called for the introduction of a wealth tax to boost government finances instead.

“They’ve got to make different choices. And of course, people may vote with their feet at the next election,” she added.

“Labour get one shot to get this right.”

TUC general secretary Paul Nowak told the BBC he was ”really concerned” by the impact of means testing winter fuel payments.

He said he wanted more support for pensioners but stopped short of calling on the chancellor to reverse her decision.

Fran Heathcote, the general secretary of the PCS union raised the prospect of industrial action over government cuts.

She said: “I can see a situation where, if they continue along the line that they’re, they’re heading with, with not just winter fuel payments but with social security and benefits more generally, there will be a real backlash and that could take the form of industrial action… because lots of unions represent low paid workers.”

Speaking on Sunday with the BBC’s Laura Kuenssberg in his first major interview in Downing Street, Sir Keir said his new government was “going to have to be unpopular” as he defended his “tough” decision to cut winter fuel payments.

He accused previous governments of avoiding confronting the cost of the winter fuel payment.

“When we talk about tough decisions, I’m talking about… the things the last government ran away from,” he said.

Chancellor Rachel Reeves has maintained the policy is a necessary move to fill a £22bn “black hole” in the public finances left by the previous government – a claim the Conservatives have challenged.

But some Labour MPs have urged the government not to go forward with the policy.

Some 11 Labour MPs were among the 27 who signed an early day motion – formal motion submitted for debate in the Commons – describing the plan as “a bureaucratic and unpopular means test” for pensioners.

One Labour MP told the Guardian, which reported the rebellion could involve as many as 50 Labour MPs, said: “I’d expect the vast majority of anyone who does rebel to abstain, and remain inside the tent. Abstention is the new rebellion.”

Although the vote is likely to go through, Sir Keir has not commented on the potential punishment for rebels ahead of the vote.

But when asked by the BBC’s Laura Kuenssberg if he would suspend rebelling MPs from the parliamentary party, he said that was “a matter for the chief whip”.

While the decision only covers England and Wales, the Scottish government has also said it would end pensioners’ universal entitlement to the payment.

The benefit is separate from other support such as Cold Weather Payments, and the Warm Home Discount scheme.

Additional reporting by business reporter Lora jones