MPs who voted for and against assisted dying have urged their respective sides not to take the “extraordinary risk” of forcing through the bill using an obscure parliamentary procedure if it continues to be blocked by the Lords.

Two Labour MPs have written a warning letter to colleagues in the crucial hours before the next vote on Friday: Gareth Snell, who voted in favour of the bill, and Meg Hillier, who voted against.

They said MPs were being presented with a “this or nothing” ultimatum and that invoking the Parliament Act to override the Lords would lead to “a constitutional showdown” with far-reaching consequences.

“Our primacy as the elected house is more than a right to enforce our will; it is a responsibility to exercise our power with the greatest of care,” Snell and Hillier wrote.

But in a countering letter, a Labour MP and a Conservative MP argued that the Parliament Act would only be used as a last resort, if the Lords sought to block the stated will of the Commons, as happened with the last version, when it was talked out by a handful of peers who tabled a huge number of amendments.

Sarah Champion and Kit Malthouse, both of whom backed the last bill, said they were happy for the Lords to suggest improvements to the new version, but that the Parliament Act was necessary to ensure “the unelected Lords cannot repeatedly block legislation passed by the elected house”.

The prime minister, Andy Burnham, has already confirmed he will not cast a vote on the terminally ill adults (end of life) bill so as not to “unduly influence the debate”.

The private member’s bill, originally sponsored by Kim Leadbeater, has been revived by another Labour MP Lauren Edwards. It had passed last year by a majority of 23 in the Commons. Supportive MPs and peers say they can use the 1911 Parliament Act to override the Lords and pass the bill should it be voted through again by the Commons.

But some MPs have expressed uneasiness at the use of the act to bypass the House of Lords on such a serious issue. The bill would allow adults with a terminal illness with less than six months to live to end their lives, after the approval of a panel of experts.

Since 1949, when it was revised, the Parliament Act has been used to enact just a handful of laws that have not had the consent of the Lords, including decriminalising homosexuality and banning foxhunting.

After a session of parliament ends, a bill must be reintroduced and passed again in the new session to trigger the act’s override mechanism. It must be exactly the same version of the bill as previously passed by the Commons.

In their letter to MPs, Snell and Hillier said the determination of the bill’s backers to use the Parliament Act meant there would be no possibility of “practical or worthwhile amendments” being added, despite concerns from hospices, medical professionals, legal bodies and others.

“This is an extraordinary risk for us to take,” they wrote. “We know that the colleagues who have brought the bill forward did so in good faith. They have sought to start a conversation many feel is overdue about an issue that is manifestly of interest to the public.

“However, the consequences of what may happen this week go much further. We both want the House of Lords to fulfil its duties, but bringing back an identical bill devoid of the previously agreed amendments sets up a constitutional showdown through an issue which deserves much more thoughtful consideration.”

In their letter, Champion and Malthouse said that Edwards and other bill sponsors had tabled some amendments to improve the original bill, and that they were open to these being debated and voted on by peers.

In a separate statement, Edwards said the measure was only having to be tabled and debated again “because a small number of peers chose to prevent any votes taking place on the bill earlier this year and so blocked its passage. That was undemocratic and brought one of the most significant national conversations we have had as legislators to an abrupt halt.

“There is a real human cost to the delay in passing this legislation and correcting the injustices and cruelty of the current law.”