The way proposed legislation on assisted dying is set to go through Parliament is “utterly inadequate” an MP has said, after she put her name to a bid to halt the plans going through the Commons.

Liberal Democrat MP Munira Wilson told the PA news agency that she is “concerned about the process or lack thereof” over what could be a “monumental change in legislation”.

She is one of a group of cross-party MPs who have supported an amendment which could be considered on Friday and which would “decline” to give a second reading to the Terminally Ill Adults (End of Life) Bill. Whether or not it is voted on would depend on whether it is selected by the Speaker.

The amendment, detailed on Tuesday’s Commons order paper – and also backed by Labour MPs Anna Dixon, Polly Billington, Josh Fenton-Glynn and Uma Kumaran, as well as Conservative Dr Ben Spencer – raises concerns about the ability to debate and scrutinise the matter and calls for an “independent assessment” of the provision of palliative care.

Kim Leadbeater, the Labour MP who has proposed the plans, has said that “Parliament would be failing in its duty” to not address a “long overdue” reform.

Ms Wilson told the PA news agency: “I’m concerned about the process or lack thereof around such a monumental change in legislation. I think the way we’ve got here and the way it’s going to go through Parliament is utterly inadequate.”

Ms Wilson, the MP for Twickenham and the party’s spokesperson on education, children and families, went on: “I think there should have been pre-legislative scrutiny, and consultation.

“There are huge questions still to be answered … around implementation in an over-stretched NHS and court system, around some of the inequalities it could create, particularly when palliative care is so patchy.”

She said the issue also throws up “big legal questions” that she does not think will be “adequately addressed” through the process of legislating a Private Members’ Bill.

She added: “I absolutely think we need a debate and need to consider legislation on this issue on the grounds of compassion and personal autonomy – but I just don’t think the way this Bill has been brought about … is the way to do it.”

Concerns have been raised about the level of scrutiny the legislation will get as a Private Members’ Bill rather than a Government Bill.

The amendment reads: “This House declines to give a Second Reading to the Terminally Ill Adults (End of Life) Bill because the House’s procedures for the consideration of Private Members’ Bills do not allow for sufficient debate on and scrutiny of a Bill on a matter of this importance”.

It also “recognises the importance of having a fully-informed debate and vote on assisted dying, which should be subsequent to an independent review of and public consultation on the existing law and proposals for change” and calls for an “independent assessment” of palliative care.

I believe Parliament would be failing in its duty if it did not take this opportunity to address a reform that is long overdue and has overwhelming public support

Whether or not the amendment is debated will depend on whether it is selected by the Speaker of the House of Commons, Sir Lindsay Hoyle.

The MPs who have tabled it have suggested that if it is selected, then it will be voted on during Friday’s session, ahead of the vote on the actual legislation.

If the amendment is selected and backed by a majority of MPs, then it could prevent the Bill from moving to a vote, they say.

It is understood debate on the main Bill would go ahead, with this amendment, if chosen, being debated as part of that.

MPs are due to get their first vote on the plans on Friday, after they were brought forward by Labour MP Kim Leadbeater.

Ms Leadbeater said in a statement: “The selection of amendments is entirely a matter for the Speaker, but it’s clear that the amendment in question is intended to prevent this vital issue being debated at all.

“I believe Parliament would be failing in its duty if it did not take this opportunity to address a reform that is long overdue and has overwhelming public support.

“As the Leader of the House, Lucy Powell, has said, my Private Members’ Bill will have at least as much time for debate and scrutiny as any other piece of legislation. I look forward to starting that process with a respectful and compassionate debate on Friday.”

The vote on Friday will be a free vote allowing MPs to decide in line with their conscience, and unwhipped by their parties.