No 10 is braced for a potential defeat in a Labour conference vote to condemn cuts to the winter fuel allowance, as major trade unions line up to back a motion to reverse Rachel Reeves’s decision.

Led by Unite and the Communication Workers Union (CWU), trade unions are expected to force a debate and vote at conference later this week to condemn the decision to axe the winter fuel allowance for all but the poorest pensioners. Unison and the GMB are understood to be likely to back a motion if a form of words can be agreed.

The timing of the vote has not yet been agreed and allies of Starmer will hope to push it to the last day of conference.

Though the vote will be non-binding, a show of dissent from unions and delegates would cast a difficult shadow on Labour’s first conference in government for 15 years.

The Guardian understands Starmer is expected to address unhappiness within Labour ranks over the decision to cut the payment, arguing the government had no choice given the tight fiscal situations.

Unite has proposed a motion to condemn the cut that is likely to end in a revised compromised motion agreed with other trade unions, similar to a motion that passed at the TUC conference. The initial wording of the motion calls on the government to U-turn in the October budget by “reversing all cuts to the winter fuel allowance”.

The backing of major unions would be likely to give the motion enough support to pass conference floor, despite the fact the vast majority of Labour member delegates at conference are supportive of Starmer’s leadership, without a significant leftwing bloc.

Unite and many Labour MPs are unhappy with the government’s decision to cut the fuel allowance. Many of the major trade unions have significant numbers of retired members sections who would be affected by the cuts.

Unite-funded billboards calling on ministers to reverse the cut were unveiled in Liverpool on Sunday. The cut for all but the poorest pensioners receiving pension credit caused widespread anger among Labour MPs when it was voted on in parliament.

Speaking on Sunday Morning with Trevor Phillips on Sky News, the Unite general secretary, Sharon Graham, attacked the “cruel policy” and called on the prime minister to ditch it. “I’d like him to say that he’s made a misstep and to reverse that policy. I’d also like him to say that we’re not going to take this country down austerity mark 2,” she said. “People voted for change. They need to see change.”

She added: “The reality here is it’s a misstep. You’ve got a situation where the poorest in our society, the first thing that Labour does is take away the winter fuel allowance from the poorest in our society while they leave the most wealthiest people pretty much untouched.”

Writing in the Observer, the Unite leader said the government’s first steps were critical and that about-turns were “absolutely necessary”. “Dying in an early ditch for policies most people hate is not only silly politics, but it can also set the public mood,” she wrote.

Matt Wrack, the general secretary of the Fire Brigades Union, said the cut was “politically inept” and “out of touch”, and said the government would face the blame when people died over the winter. He told a fringe meeting at conference: “Ordinary voters are baffled by the decision. Within the first few weeks of the government, there are some worrying trends.”

Starmer met union general secretaries in Liverpool on Saturday afternoon before the conference opened. He has said cutting the winter fuel allowance is necessary because the Conservative government left a £22bn hole in the public finances.

Graham had earlier accused the chancellor of being too focused on fiscal prudence at the expense of economic reform and growth. In an interview with the House magazine published as the conference got under way in Liverpool, she said: “You want a Labour government to come in and not just manage better. You want them to come in and be visionary.

“I worry that the Treasury, particularly, has got a hand in stopping some of the vision, and certainly stopping some of the investment. That’s what you’d have to conclude from what I’m seeing.”

Graham, who has been critical of Starmer and Reeves, renewed her call for ministers to rip up the fiscal rules so they can borrow more to invest in infrastructure and public services. She has made the remarks as Reeves’s first budget approaches in October and after Andy Burnham, the mayor of Greater Manchester, said the Treasury needed to change the way it thinks to achieve its goal of promoting growth.

In an interview with the Financial Times, Burnham said “there are a number of ‘growth tests’ looming – not least on rail infrastructure – and we will find out soon whether the Treasury is able to transform itself into the growth department”.

He added that the Treasury “needed to understand that growth came from giving hope and planting seeds, rather than saying no to everything”.

Reeves has vowed to lead the UK’s most “pro-growth” Treasury but Downing Street has repeatedly said that the budget in October will involve some painful decisions, which are expected to include tax rises.