Unite general secretary Sharon Graham directly told the Prime Minister that he should reverse the controversial policy.
But Sir Keir was showing no signs of backing down.
Downing Street said there were no plans to water down the restriction to the special payments.
There was no discussion of softening the impact of the winter fuel cut at Cabinet on Monday, No10 said after a Home Office minister suggested the policy may be tweaked.
Asked whether Dame Diana Johnson had been “freelancing” when she said mitigations were being looked at by ministers, a No 10 spokeswoman said: “I think it was promptly corrected.”
She added: “The Prime Minister has always been clear that he will always be straight with the public about the tough decisions that this Government has to take.”
Asked whether Sir Keir was worried that pensioners may die as a result of the cuts, the spokeswoman said “the …