Nearly 40 Labour MPs have signalled they are still prepared to vote against Sir Keir Starmer’s welfare cuts, despite the prime minister offering significant concessions to avoid a damaging rebellion.

Thirty-nine Labour MPs have backed a fresh amendment to the updated welfare bill, which instead of cutting benefits for existing claimants, now only restricts them for new ones.

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The number is a significant drop from the 127 Labour MPs who last week signed a separate amendment that would have killed the legislation and delivered a severe blow to Sir Keir’s authority if it passed.

In an attempt to minimise the looming rebellion, the prime minister watered down his original welfare proposals to minimise the impact on existing claimants.

On Monday, Work and Pensions Secretary Liz Kendall confirmed that all existing claimants of the personal independence payment (PIP), the main disability benefit, will be protected from changes to eligibility, which has been tightened under the original plan.

The combined value of the standard Universal Credit allowance and the health top-up will rise “at least in line with inflation” every year of this parliament, while an additional £300m for employment support for sick and disabled people in 2026 has been announced, which will rise every year after.

Ms Kendall also promised a consultation into PIP – “co-produced” with disabled people – will be published next autumn, which was a key demand of the rebels.

Analysis by the government published yesterday revealed the new welfare offer would still push 150,000 more people into poverty by 2030 – down from the 250,000 estimated under the original plan.

Ms Kendall said the U-turn on welfare cuts will cost taxpayers about £2.5bn by 2030 – less than half the £4.8bn the government had expected to save with its initial proposals.

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However, several Labour MPs indicated they would still vote against the bill, with some saying it would create a two-tier benefits system that treats existing claimants and new claimants differently.

The fresh amendment signed by the 39 Labour MPs calls for the bill to be dropped over concerns that there has not been a proper, formal consultation with disabled people – and the additional employment support funding will not be in place until the end of the decade.

It is up to Sir Lindsay Hoyle, the House of Commons Speaker, to decide whether to select the amendment when the bill is put to a crunch vote later today.

Nadia Whittome, the Labour MP for Nottingham East and on the party’s left, said the concessions “aren’t enough”.

She told Sky News’ Kamali Melbourne this morning: “I think it’s very telling that not a single disabled people’s organisation supports the bill, even since the concessions, there’s a lot that we don’t know about how that will work in practice.

“But what we do know is that anybody scoring less than four points in any category in their PIP assessment will not be eligible for support – that includes people who need help cutting up food, need help dressing, washing below the waist. They will no longer be eligible for PIP in future.

“By the government’s own calculations that could push 150,000 people into poverty… it’s actually likely to be much higher.”

Sarah Owen, the Labour MP for Luton North and the chair of the Women and Equalities Committee, questioned whether a “three-tier” benefits system could be created, when taking into account the fact that a government review is being carried out into the PIP assessment system by minister Stephen Timms.

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Business Secretary Jonathan Reynolds denied claims of a “three-tier” system, saying: “I’ve seen these claims. I don’t accept this.

“It’s entirely normal for when we have significant changes to the welfare state, existing entitlements to be grandfathered.”

He also urged his colleagues to vote for the bill, arguing the government was now in a “stronger position” than it was last week after making concessions over its plans.

“I’d ask them to support the government on that basis, because clearly what we’ve got here is something which is better than the existing system,” he said.