Labour MPs who are opposed to legalising assisted dying believe the momentum is swinging behind their side of the campaign, Sky News has learnt.

MPs are currently weighing up whether to back a change in the law that would give terminally ill people with six months to live the choice to end their lives.

At a meeting in parliament on Wednesday, Sky News understands Labour MPs on the opposing side of the argument agreed that those who were undecided on the bill were leaning towards voting against it.

One Labour backbencher involved in the whipping operation for the no camp told Sky News: “The undecideds are breaking to us, we feel.”

The source said that many of those who were undecided were new MPs who had expressed concerns that not enough time had been given to debate the bill.

“They feel they are too new to be asked to do something as substantive as this,” they said.

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Issues that were being brought up as potential blocks to voting for the legislation include that doctors would be able to suggest assisted dying to an ill patient, they said.

The source added: “We were elected to sort the NHS out rather than assisted dying.

“And there is no going back on this – if any doubt, you should vote it out.”

The Terminally Ill Adults (End of Life) Bill, put forward by Labour MP Kim Leadbeater, is due to be debated on 29 November, when MPs will be given a “free vote” and allowed to vote with their conscience as opposed to along party lines.

In a recent letter to ministers, Cabinet Secretary Simon Case said the prime minister had decided to “set aside collective responsibility on the merits of this bill” and that the government would “remain neutral” on its passage and the matter of assisted dying.

There has been much debate about the bill since its details were published on Monday evening, including that the medicine that will end a patient’s life will need to be self-administered and that people must be terminally ill and expected to die within six months.

Ms Leadbeater, who has the support of former government minister Lord Falconer and ChildLine founder Dame Esther Rantzen, believes her proposed legislation is the “most robust” in the world and contains safeguards she hopes will “reassure” those who are on the fence.

They include that two independent doctors must confirm a patient is eligible for assisted dying and that a High Court judge must give their approval.

The bill will also include punishments of up to 14 years in prison for those who break the law, including coercing someone into ending their own life or pressuring them to take life-ending medicine.

She has also argued the fact terminally ill patients will have to make the choice themselves and administer the drugs themselves “creates that extra level of safeguards and protections”.

However, several cabinet ministers – including Health Secretary Wes Streeting and Justice Secretary Shabana Mahmood, who would be responsible for the new law – have spoken out against the legislation.

Mr Streeting, who has said he intends to vote against the bill owing to concerns that people might be coerced into taking their own lives, announced a review into the potential costs of assisted dying if it is implemented.

The health secretary warned that a new assisted dying law could come at the expense of other NHS services – and that there could be “trade-offs” elsewhere.

Sky News understands Ms Leadbeater has said she is “disappointed” by Mr Streeting’s comments about the bill.

And another Labour MP who is voting for the legislation told Sky News they believed Mr Streeting had “overstepped the mark”.

“I think it’s a bit of a false exercise,” they said.

“It’s definitely going to raise eyebrows – it’s one thing to sound the alarm but he is purposefully helping the other side.”

The MP said that while it did feel “the momentum is moving away from us, a lot of it will come down to the debate and argument in the chamber”.

“Some of the scaremongering tactics might backfire,” they added.

“It’s still all to play for but it’s undoubtedly true the other side seems to be making headway at the moment.”

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A source close to Mr Streeting told Sky News: “Wes has approached this issue in a genuine and considerate way, setting out his own view while respecting others’ views.”

As a private member’s bill that has been put down by a backbencher rather than a government minister, the legislation will not receive as much time for consideration as a government bill – but proponents say it can always be amended and voted down at later stages.

At Prime Minister’s Questions on Wednesday, Tory MP Sir Alec Shelbrooke questioned whether enough time had been set aside to debate the bill and urged Sir Keir Starmer to allow two days, or 16 hours, of “protected time” to “examine and debate” the legislation before the vote.

Sir Keir replied: “I do think there is sufficient time allocated to it but it is an important issue.”