If the bill to legalise assisted dying is thrown out by MPs later this month then “the conversation ends” on the subject, with dreadful consequences for many terminally ill people, the MP leading the process has warned.

Speaking at a press conference organised by supporters of the bill, which has its third reading on 25 April when MPs will vote on amendments, Kim Leadbeater said her colleagues in the Commons have a “duty as parliamentarians to change the law now”.

The Labour MP dismissed the idea that if the bill was defeated, the subject could return as government legislation or a royal commission, noting the long gap between the last time assisted dying was debated in the Commons, in 2015, and her efforts.

“What worries me is, if the bill doesn’t pass, the conversation ends, and that would be really dreadful for so many people, for so many reasons,” she said.

A lengthy and sometimes gruelling committee stage in which a group of MPs considered amendments to the bill has already brought significant changes, including scrapping the requirement for a high court judge to scrutinise every case in favour of an expert panel.

In a last-minute concession just before the committee stage ended, Leadbeater proposed pushing back the earliest implementation of the law to 2029, two years later than envisaged.

But the main element of eligibility remains the same, with assisted dying only available to terminally ill adults in England and Wales with fewer than six months to live.

The third reading vote on 25 April carries some uncertainty, although the second reading vote in November passed with a majority of 25, prompting opponents of the bill to claim some MPs have changed their minds.

Speaking at the same press conference in parliament with Leadbeater, Sir Max Hill, a former director of public prosecutions who backs the bill, said the “dial has turned” in terms of public opinion as he warned MPs against seeking more delay.

He said: “There is time for anyone on receipt of the republished bill to really consider it carefully – kicking this can down the road really is no solution for anybody.”

Leadbeater said criticism that scrutiny of the bill had been rushed was “utter nonsense”.

Another Labour MP, Marie Tidball, who was on the bill scrutiny committee and is a disability rights advocate, said she had been happy with an amendment to guarantee independent advocates to support people with learning disabilities, autism or mental health conditions, and that she would support it at third reading.

Tidball said: “I can say, as someone who has looked at legislative scrutiny over the course of the last 20 years, this is the most extraordinary, deliberative cross-party process I’ve ever seen.”

Some MPs, however, remain opposed. In a statement released by opponents of the bill in response to the press conference, Labour MP James Frith called the bill “a mess, with significant issues of concern where there had been promises of scrutiny and improvement”.