Ministers have “negligently underestimated” how many pensioners will “fall through the cracks” following cuts to winter fuel payments, the Tories have claimed.

Shadow work and pensions secretary Helen Whately also urged Labour frontbenchers to press Chancellor Rachel Reeves to “think again” about means-testing the payments worth up to £300.

From this winter, only people on pension credit or certain other benefits will receive the winter fuel payments while more than nine million others are set to be stripped of the allowance, which could save the Government more than £1 billion.

The Government has insisted the move is necessary to help fill a “£22 billion black hole” in the public finances inherited from the Tory government.

The Social Security Advisory Committee (SSAC) last month said the savings from limiting the winter fuel allowance to only the poorest pensioners are unclear and could be outdone by a rise in those seeking pension credit.

The SSAC, which provides statutory advice to ministers on benefits, also criticised the Government for not providing an impact assessment of its plans before they were brought into law.

Speaking during an urgent question on Tuesday, work and pensions minister Emma Reynolds apologised to the Commons for the delay in the Government replying to concerns raised by the SSAC and said a response should be issued this week.

For the Conservatives, Ms Whately said: “This Government made a choice to take away the winter fuel payment from 10 million pensioners this winter and to rely on the notoriously underclaimed pension credit as a system of means-testing it.

“This choice will make life harder for pensioners across the country.

“It will see 750,000 of the poorest pensioners miss out on much-needed help with the cost of heating and, according to the party opposite’s own research, could lead to 4,000 additional deaths this winter.

“The Government knows this, that’s why they haven’t done an impact assessment and perhaps that’s why after seven weeks they still haven’t responded to the concerns of their own advisory committee.”

We didn't want to take the decision to means-test winter fuel payments but we've had to do this, to take some difficult decisions, in order to clear up the mess.

She added to Ms Reynolds: “Does she accept that her Government has got this wrong? Does she recognise that they have negligently underestimated how many people will fall through the cracks?

“I suspect that deep down that she is worried, as I am, about pensioners who can’t afford to heat their homes.”

Ms Whately added: “Will she go back to her Chancellor one more time and try and make her think again?”

Ms Reynolds replied: “I do apologise for the delay in responding to the committee’s letter. It is regrettable.

“The initial delay was because we were waiting for the OBR (Office for Budget Responsibility) to come forward with their costings of the policy.

“And then there was another unexpected delay.”

The minister also said the Government has done “everything in line” with the duty to provide an equality analysis of the decision.

Ms Reynolds noted Ms Whately had not apologised for the previous Tory administration’s record, adding: “We didn’t want to take the decision to means-test winter fuel payments but we’ve had to do this, to take some difficult decisions, in order to clear up the mess, to tackle the fiscal inheritance and start rebuilding our public services, which pensioners across the country and many, many others rely on.”

Independent MP Richard Burgon (Leeds East) later urged ministers to “think again” on the policy, as he said the cut would save around 0.1% of Government spending.

Mr Burgon, who lost the Labour whip in July for backing an SNP motion on welfare policy, said: “On this occasion I do believe we got it wrong, so could the Government rethink on this issue?”

Liberal Democrat work and pensions spokesperson Steve Darling asked the Government to extend the deadline to apply for pension credit beyond December 21, in light of the “unexpected delays” .

Ms Reynolds replied: “I’m afraid I can’t commit to extending the deadline.”

She added: “Those claims can be backdated by three months, and anyone who is eligible for pension credit within the qualifying week will also be passported to other benefits such as the winter fuel payment.”

Conservative former minister Sir Christopher Chope said: “What is the point of having a Social Security Advisory Committee if the Government doesn’t listen to its advice and take its advice? Would it not be better to abolish the Social Security Advisory Committee if the Government is intent on ignoring it.”

Ms Reynolds replied: “No.”