Sir Keir and Chancellor Rachel Reeves have been heavily criticised for the move, including by some Labour MPs and Age UK.
But the prime minister said on Monday: “We have found a £22bn black hole in the economy. And we’ve got to fix it.
“What we’re not going to do is pretend it isn’t there or paper over it. That’s what the last government did, and it made it worse. That means we’ve got to make tough choices.
“I don’t want to cut the winter fuel allowance. I don’t think anybody in the government wants to do that. But we’ve got to fix the foundations of our economy.”
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Are we set for tax rises?
He said after fixing the foundations of the economy “we can build a build a better future that pensioners and so many other people voted for in this election”.
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“This is a tough decision, not a decision I want to make, but I’m absolutely determined will stabilise the economy and fix the foundations,” he added.
Labour MP Jessica Asato, newly elected in July, wrote to Work and Pensions Secretary Liz Kendall last week calling for changes to the policy, specifically to increase the number of people who can claim it.
The Conservatives and Lib Dems have hit out at the plan, with Lib Dem leader Sir Ed Davey calling it the government’s “first big mistake”.
Both parties had called for a vote on axing the payments but the government has refused to hold one.
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The UK’s leading charity for older people, Age UK, has written to Ms Reeves with a detailed plan suggesting the allowance should be paid to two million more pensioners who are on other benefits, including housing benefits, council tax support, attendance allowance and carers’ allowance.
On Sunday, Commons leader Lucy Powell told Sky News’ Sunday Morning With Trevor Phillips the move was necessary as the economy could have crashed if the government had not found the savings.