Diane Abbott has warned it could soon be cheaper for GPs to encourage seriously unwell patients to “sign on the dotted line for assisted suicide” than to find them a place in a hospice.

The senior Labour MP voted against changing the law because she fears vulnerable people will get swept up in the assisted dying route when “actually what they really need is access to hospice care and proper end-of-life care”.

The Commons backed a bill proposed by the Labour MP Kim Leadbeater by 330 votes for to 275 against on Friday, in a significant move towards giving eligible people greater choice over the way they die.

Leadbeater has given repeated assurances that the bill will be measured and appropriate safeguards will be put in place to ensure that nobody is pressed into assisted dying.

The health secretary, Wes Streeting, faced calls during the parliamentary debate to “put firm commitments on palliative care on the table” whether or not the bill becomes law.

Already, some MPs who backed the bill on Friday have signalled they could consider changing their mind further along the process because of their concerns around safeguarding.

Raising questions once again over the state of palliative care in England and Wales, Abbott told the BBC’s Sunday with Laura Kuenssberg programme: “We’re moving to a situation where it will be cheaper for a GP to get a very ill person to sign on the dotted line for assisted suicide than to find them a place in a hospice.”

Meanwhile, Pat McFadden, the chancellor of the duchy of Lancaster, indicated on Sunday that people may have to pay to fund an assisted dying system.

When asked if it would be entirely state-funded, he told Times Radio: “Again, all of that will be considered during the committee stage. The government will have to look at the bill much more seriously now that it’s been passed by parliament. This was a private member’s bill, remember, not a government bill. But it’s for the government to enact the will of parliament if this bill goes through all those other stages that I said.”

When pressed two more times if there was a possibility at all, the cabinet minister said: “Look, I think all that still has to be considered. As you know, people currently have to pay for this themselves if they go to Switzerland.

“So all those questions of costs, safeguards, all the issues that have been raised have to be considered during the committee stage, the clause-by-clause examination of the bill. And that’s the right way to do it because it’s a huge change. And you could see that on the faces of the MPs who are voting for it or against it on Friday.”

There were three Conservative MPs and 18 Labour MPs for whom no vote was recorded on Friday.

Josh Fenton-Glynn, the Labour MP for Calder Valley, said he had abstained because “as it stands I don’t think the safeguards are strong enough”.

• Assisted dying
• Diane Abbott
• news