But it remains to be seen whether this will be enough to stop the rebellion after the number of Labour MPs signing an amendment opposing the cuts rose again, with 126 now signed up.

This is enough to defeat the Government in the vote, if opposition parties such as the Conservatives also vote against the government. And the fact that the numbers keep on rising suggest Number 10’s efforts to halt the rebellion are failing.

Sir Keir Starmer is understood to be personally calling Labour backbenchers today to plead for their support.

Downing Street insiders said talks were taking place with Labour MPs about the legislation after 126 of them publicly backed a move to block the legislation.

The first vote on the Universal Credit and Personal Independence Payment Bill is due to take place on Tuesday and a concerted effort has been launched by ministers to win round potential rebels.

A No 10 source said: “The broken welfare system is failing the most vulnerable and holding too many people back.

“It’s fair and responsible to fix it. There is broad consensus across the party on this.”

The source insisted the reforms were “underpinned by… Labour values”.

They said: “Delivering fundamental change is not easy, and we all want to get it right, so of course we’re talking to colleagues about the Bill and the changes it will bring, we want to start delivering this together on Tuesday.”

Deputy Prime Minister Angela Rayner said talks between backbenchers and the Government were “ongoing” as six more Labour MPs added their names to the rebel amendment that would halt the legislation in its tracks.

The reasoned amendment argues that disabled people have not been properly consulted and further scrutiny of the changes is needed.

The new signatories include the Commons Environmental Audit Select Committee chairman Toby Perkins, Stoke-on-Trent Central MP Gareth Snell, Newcastle upon Tyne MP Mary Glindon and Tamworth MP Sarah Edwards.

North Ayrshire and Arran MP Irene Campbell and Colchester MP Pam Cox, both of whom won their seats in the party’s 2024 landslide election victory, have also added their names.

The new names take the total number of Labour backbenchers supporting the amendment, tabled by Treasury Select Committee chairwoman Dame Meg Hillier, to 126.

The plans restrict eligibility for the personal independence payment (Pip), the main disability payment in England, and limit the sickness-related element of universal credit.

The Government hopes the changes will get more people back into work and save up to £5 billion a year.

Existing claimants will be given a 13-week phase-out period of financial support, a move seen as a bid to head off opposition by aiming to soften the impact of the changes.

But the fact so many Labour MPs are prepared to put their names to the “reasoned amendment” calling for a change of course shows how entrenched the opposition remains.

One backbencher preparing to vote against the Bill told the PA news agency: “A lot of people have been saying they’re upset about this for months.

“To leave it until a few days before the vote, it’s not a very good way of running the country.

“It’s not very grown-up.”

They said that minor concessions would not be enough, warning: “I don’t think you can tinker with this. They need to go back to the drawing board.”

The Daily Telegraph reported that potential concessions being considered include a commitment to speed up payment of support to help people back into work and offering assurances that reviews of policies in this area will be published.

Meanwhile, The Times reported some MPs opposed to the plans had blamed Sir Keir’s chief of staff Morgan McSweeney and suggested the time had come for “regime change” in Downing Street.

Asked about attacks on Mr McSweeney, trade minister Douglas Alexander said: “I’m much less interested in the gossip about SW1 than whether this legislation works on the streets, in the towns, in the communities right across the country.”

He said it was “for the Prime Minister to make his judgments” about who works in Downing Street but the fact is that team delivered us an historic victory only last July, against expectations”.

Mr Alexander told Sky News: “The task of government is hard, there are always going to be people with strong opinions on all sides of an issue like welfare reform.”

He told ITV’s Good Morning Britain: “If there are practical ways that we can improve this legislation, we should.

“We should do it not to buy off rebels, but because it’s a Labour thing to do and that’s the conversation that I expect ministers will be engaged in in the coming days.”

Analysis by the Institute for Fiscal Studies (IFS) think tank indicated overall, 800,000 fewer working-age people are expected to receive a Pip daily living award in 2029–30 due to the reforms.

The tighter criteria are set to lead to 430,000 new applicants – who would have received an award without reforms – receiving no award, and 370,000 existing claimants losing out following reassessment.

Most of the 800,000 losers will receive £3,850 per year less in Pip.

But even if the reforms are fully implements, official forecasts still suggest that the number of working-age claimants of Pip or its predecessor in England and Wales will rise from 3.1 million in 2024–25 to 3.9 million in 2029–30.

The 2.2 million existing claimants of the health element of universal credit who are expected to still be claiming in 2029–30 are estimated to see a £450 real decline in their support in that year due to the freezing of the payment.

There are also set to be 700,000 new claimants who will typically receive £2,700 a year less than they would have done under the current system, the IFS said.

The changes are aimed at increasing incentives to work for people who are able to, but IFS senior research economist Eduin Latimer said: “The changes may lead to an overall increase in employment, though any boost to employment income is unlikely to come close to offsetting the direct income losses experienced by affected claimants.”