Reeves: Cutting child poverty in 'our DNA' but can't lift benefit cap

She added that free breakfast clubs, additional nursery places and a rise in minimum wage would improve people's living standards.

However, she would not commit to removing the benefit limit currently arguing "unfunded commitments" crash the economy and that "ends up costing the most vulnerable in society even more".

The benefits cap, announced by George Osborne in 2017 when he was Chancellor, limits Universal Credit and child tax credits to the first two children. The SNP have opposed the policy since it was introduced and last week repeated calls for it to be axed.

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When it was put to her that removing the limit would lift 500,000 children out of poverty, Ms Reeves said: "It costs more than £3 billion a year. And we were really clear during the election that we were not going to make spending commitments without being able to say where the money was going to come from.

"If I said to you now: 'We're going to make those changes this year or next year or the year after', you would rightly say: 'Where's the money going to come from for that?'

"If we're not able to say where the money is going to come from, we can't promise to do it. And that's true when it comes to the two child limit, and anything else."

She added that Labour's policies would still help the poorest in society: "If you ask: are we going to lift kids out of poverty? Absolutely, we are. I look at the some of the things that we've committed to do and that we will do.

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"A free breakfast club for all primary schools so that all children get a good breakfast in the morning, and to help their mums and dads be able to take more hours at work, or to get a job. The creation of 3,000 additional nurseries with 100,000 places to help again working parents be able to work to provide for their families.

"The New Deal for Working People to turn the minimum wage into a real living wage, banning the exploitative zero hour contracts. These are all things that have a material impact on child poverty.

"Previous Labour governments have lifted kids out of poverty. It is what is in our DNA. We will do that."

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She said that promising to spend without funding the policy would crash the economy: "I'm not willing to make unfunded commitments because what happens when you make unfunded commitments, whether they are around tax or spending, is the economy crashes.

"And that financial market turbulence ends up costing the most vulnerable in society even more through higher mortgages and higher rents."

Labour is under pressure from some of its MPs and from many trade unions to lift the two child benefit cap.

Appearing on a panel on the same BBC show Labour MP Zarah Sultana urged the government to remove the cap immediately. She pointed to former Prime Minister Gordon Brown and Scottish Labour leader Anas Sarwar backing the lifting of the cap.

"I'd like the party to also adopt scrapping the two child benefit cap. This is something that Gordon Brown has called for. This is something that Anas Sarwar and Scottish Labour have policy for," Ms Sultana said.

More than a dozen backbenchers are understood to support an amendment to the King’s Speech, and the SNP has also tabled an amendment to scrap the cap, which with a few exceptions prevents parents from claiming universal credit or child tax credit for a third child.

The MP for Canterbury, Labour’s Rosie Duffield wrote in The Sunday Times that the cap was “sinister and overtly sexist” and had been her main motivation in standing for parliament.

She also criticised the so-called “rape clause”, which provides an exception for children conceived as a result of an attack.

“The authors of this policy are telling women: disclose to a series of total strangers that your third or any subsequent children are the result of rape and we will pay you after all,” she said.

The two-child benefit cap affects 1.6 million children across the UK, according to the latest figures from the Department for Work and Pensions.

Many of the charities and organisations consulted by the work and pensions secretary, Liz Kendall, on an anti-poverty taskforce set up last week have called for the cap to be abolished.

Save the Children said that “scrapping the two-child limit is the most cost-effective way to reduce child poverty” and the TUC said “punitive policies like the two-child limit have caused widespread misery”.

The Resolution Foundation has said the “costs are low compared to the harm that the policy causes, and scrapping the two-child limit would be one of the most efficient ways to drive down child poverty rates”.

In the same BBC interview on Sunday, Ms Reeves was also asked about reports that public sector workers in England and Wales would be given above inflation pay risses.

Reports which first appeared in The Times suggest independent pay review bodies have recommended the 5.5% rise for teachers and around 1.3 million NHS staff.

Pressed on the issue, the Chancellor said she values public service workers and "people won't have long to wait for a decision".

"There is a cost to not settling, a cost of further industrial action, and a cost in terms of the challenge we face recruiting," she told Sunday With Laura Kuenssberg, stressing her spending rules were "non-negotiable".

"We will do it in a proper way and make sure the sums add up."

She also accused the previous Conservative government for leaving the new Labour administration with the worst fiscal inheritance since the Second World War.

But former Chancellor Jeremy Hunt told Ms Kuenssberg this was "absolute nonsense" and designed to lay the groundwork for tax rises.

He said: "I was looking until a couple of weeks ago at the same numbers that Rachel Reeves is now looking at.

"It's very clear that if you are prepared to show restraint on public sector pay, as we did last year, if you're prepared to be ambitious on public sector productivity, as I was in the budget, and you're prepared to do welfare reform, which was glaringly absent from the King's Speech - if you do those three things it's perfectly possible to balance the books in a way that means taxes don't have to rise.

"Now I think it's very clear from what we've seen in the first two weeks of this Labour Government that they're not prepared to take those difficult decisions."

Mr Hunt also denied having "run away" from making decisions on public sector pay, saying: "You can criticise me for many things, but not taking tough and difficult decisions is one thing I don't think people would level at me."