A top economist has said is known across the world for the cuts which took away the allowance for millions of pensioners.
Last year, the government took the decision to means test the payment, affecting around 10 million pensioners, which has had a "much bigger" effect on his reputation, according to Paul Johnson. Mr Johnson is the head of the respected Institute for Fiscal Studies (IFS), an independent body based in London which specialises in UK tax and public policy.
He told : "I was talking to the head of an international insurance company recently who said that the one thing everyone around the world knows about this government is that it's taking money away from helping the cost of fuel for pensioners.
"So it's one of those things which actually from a sort of fiscal point of view is pretty small but has turned out, I think, to be much bigger from a political and reputational point of view than the government expected."
Research has found the cuts to winter fuel payments are better known among the public than another other Labour policy.
Pollsters More in Common found around two thirds of voters dislike the policy, while the company's director Luke Tryl described it as Labour's "original sin" and said it was a key factor in last week's local elections.
The policy is expected to save around £1.5 billion for the government but could push over 100,000 pensioners into poverty.
Mr Johnson said the action was a "perfectly sensible thing to do" given much of the winter fuel allowance previously went to wealthier people who did not require it.
Yet some Labour MPs are demanding that the prime minister scrap the move in order to avoid a Reform "wipeout" in future elections.
Some think he may be forced to reverse the cut before Christmas, when winter returns.
Last week, Labour lost almost two thirds of the seats it was defending, also succumbing in the previously safe seat of Runcorn and Helsby.
Voters were reportedly furious with the decision to remove the winter fuel payment and raised their concerns on the doorstep during the campaign.
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