Keir Starmer has said he is “not immune” to the powerful argument for scrapping the two-child benefit cap, after experts said the number of children affected by it would rise by a third in the next five years.

The Labour leader refused to set out a timeline for when he would scrap the policy, despite previously saying he would ditch it if he could.

“I’m not going to put a date on these things, but I’m not immune from just how powerful an argument this is,” Starmer said.

The policy, which was introduced by George Osborne when he was chancellor, means low-income parents are denied key benefits, including universal credit, for their third and any subsequent children born from April 2017.

The Institute for Fiscal Studies (IFS) has warned 250,000 more children will be affected by the limit when it is fully rolled out, and it is expected to rise to 670,000 before the end of the next parliament if the policy is not reformed. The two-child benefit limit currently affects 2 million children.

Starmer accused the chancellor, Jeremy Hunt, of admitting that the pledges in the Conservative’s manifesto were “completely unfunded” and cited this as a reason why many people were still living in poverty.

The Labour leader told reporters at the Port of Southampton: “By saying that the money they were pretending was there to fund their manifesto is in fact, money that’s already accounted for … that’s the problem and that bears down on poverty because once you lose control of the economy then it’s working people and children who pay the price.”

Senior Labour figures have urged Starmer to scrap the two-child benefit cap. Starmer said it was a “tough decision” but one Labour had to make because of the damage Liz Truss had done to the economy. “It would be so much worse if anybody was to repeat the mistakes of Liz Truss government,” he said.

He was speaking at the start of Labour’s “economy” week, during which the party hopes to highlight their proposals to drive investment and contrast it with the Tories “unfunded” manifesto plans.

The Tories set out plans for billions in tax cuts, which they claim would be paid for by ?12bn of savings on welfare.

Starmer also attacked Conservative ministers for urging Rishi Sunak to “go for the jugular” and launch more direct personal attacks against him.

The Labour leader said: “That’s all they’ve got left after 14 desperate years. You get to the last weeks and their only thing they’ve got left is to attack me personally, I think that tells you everything.”