Keir Starmer is under growing pressure to scrap the two-child benefit cap as more than a dozen Labour backbenchers call for it to be axed.
On Monday, the Education Secretary said they would "consider" scrapping the policy under a new child poverty tax force working across Whitehall.
The cap prevents parents from claiming benefits for any third or subsequent child born after April 2017.
Scrapping the policy would cost the current Labour government £2.5 billion, according to the Resolution Foundation think tank.
Starmer said there is "no silver bullet" to solve child poverty
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Despite a push to end the policy by some Labour MPs, a new poll shows that 60 per cent of Britons think the two-child benefit limit should be kept.
Less than three in ten (28 per cent) believe the government should abolish the policy.
There is support for keeping the cap across almost all voting and social groups including Labour who back it 50 per cent compared to 38 per cent who oppose it.
Support is highest among 2024 Conservative (81 per cent) and Reform UK (84 per cent) voters who overwhelmingly support keeping the policy.
The only group who back abolishing the ban is among 18 to 24-year-olds with 46 per cent voting to axe the policy while 32 per cent support it.
The results of the survey show that 60 per cent of Britons think the two-child benefit limit should be kept
YouGov
Older voters are far more likely to favour the policy with 69 per cent of 50 to over 65s supporting the policy.
The two-child benefit limit was introduced by Conservative Chancellor George Osborne in 2015 and has been controversial amongst Labour figures.
The cap is opposed by anti-poverty campaigners for its links to increased rates of child poverty among affected families.
Rosie Duffield is one of the latest MPs to hit out at the scheme branding it as a "social cleansing" and an "unequal piece of legislation."
She wrote in the Sunday Times: "It is a heinous piece of legislation and the reason above all others that I was driven to stand as a member of parliament… When proclamations on benefits are handed down by the great and the good in Westminster, the stark divide between the wealthy and those struggling is never more visible…"
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Speaking to Sky News on Monday, Education Secretary Bridget Phillipson said the government would "consider [lifting the cap] as one of a number of levers in terms of how we make sure we lift children out of poverty."
However, later in the day, No 10 denied the government has changed its position on the cap as the prime minister's official spokesperson told reporters: "It’s as the chancellor said yesterday, it’s as the PM I think addressed this morning as well, the government has got a certain set of fiscal inheritance that it has to deal with."
Prime Minister Keir Starmer said: "There is no silver bullet. It was a silver bullet. It had been shot a very long time ago.
"It's a complicated set of factors that I know, and I can see every day in my own constituency, to do with pay, to do with benefits, to do with work, to do with housing, to do with education, to do with health.
"And that is why you need a strategy to deal with it, which is why we set up a very strongly chaired body to drive forward that work."
The results for this story came from a YouGov survey of 2085 British adults conducted between July 8 and July 9.
