Labour’s Yvette Cooper has refused to say if she supports Sir Keir Starmer’s decision to keep the two-child benefit cap, amid growing party divisions over the issue.

The shadow home secretary said that – while the party wanted to address child poverty – “we’ve got to keep saying how we will pay for things”.

Sir Keir revealed over the weekend that he would keep the two-child benefit cap, which prevents parents fclaiming child benefits for any third or subsequent child born after April 2017.

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He had previously opposed the limit during his campaign to be Labour leader – prompting accusations of a U-turn from critics.

Sir Keir’s intervention over the weekend also prompted a fresh backlash from his MPs, with Dame Meg Hillier, the chair of the Public Accounts Committee, saying she was “never comfortable about having the child benefit cap come in” and that she would personally lobby for it to be lifted.

Rosie Duffield, the MP for Canterbury, also tweeted that it was one of the “most unpleasant pieces of legislation ever to have been passed in the UK”.

It also emerged that several shadow cabinet ministers have previously spoken out against the policy, with Labour’s deputy leader Angela Rayner describing it as “obscene and inhumane” and Jonathan Ashworth, the shadow work and pensions secretary branding it “heinous”.

Asked whether she personally supported the cap, Ms Cooper avoided the question but repeated that Labour could not make unfunded promises.

And pressed on whether Labour would spend money on public services, she said Labour had already set out areas where it would increase investment, such as funding education through scrapping tax exemptions from private schools and the non-dom tax status.

Ms Cooper also cited breakfast clubs, reforming Universal Credit and having a “long-term plan” to get people into work as measures the party would take to slash child poverty.

“We want to invest in our public services, but we’re also being really straight with people about where the funding is going to come from because we know that we’ve got to be really responsible with the public finances, and also show that we can deliver,” she said.

“I think people are fed up of promises that they think can’t be delivered.”

But pushed on whether she supported keeping the cap, Ms Cooper did not answer the question and replied: “We’ve got to be clear about what we can fund and that’s why Keir Starmer set out the position.”

Labour’s stance has prompted fears among some stakeholders, including trade unions, that its offer to the public is not bold enough nor different enough from the Tories going into the next election.

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Mick Lynch, the general secretary of the RMT union, told Sky’s Sophy Ridge On Sunday programme that Sir Keir should be “saying something about workers’ rights, he should say stuff about funding the NHS … addressing all sorts of stuff about what’s going to happen in the imbalance in our society”.

He added: “It’s a shame that Labour and others can’t show that they’re distinct from the kind of consensus that’s got us into this trouble where working people are struggling, the cost of living crisis seems to be ignored by the political class to certain extent.

“I don’t think Labour’s doing enough, we will be critical of Labour when they don’t do the right stuff and we will be supportive on the occasions that they do.

“And at the minute, many people can’t spot the difference and that’s a shame for somebody who’s probably as talented as Keir Starmer is, he’s got to show that he’s on the side of working people and progressive politics, and I don’t think we’re seeing that.”