A number of Labour MPs are increasingly doubtful that the guidance on how organisations should implement the supreme court ruling on sex as it applies in the Equality Act is workable in the real world, with some predicting it will unleash a wave of competing legal claims.

A total of 135 MPs, 69 of them from Labour, have signed a Commons motion calling for the code of practice drafted by the Equality and Human Rights Commission, approved last month, to be blocked, primarily because of worries about its impact on transgender people.

While it is very unlikely that the guidance will be stopped – that would need the government to grant a vote, which it has declined to do – there is mounting pressure from backbenchers for ministers to listen, and even to consider new legislation to come up with a solution.

Concerns among some MPs increased after the EHRC’s chair, Mary-Ann Stephenson, and its chief executive, John Kirkpatrick, were quizzed on the practicalities of the code by the Commons women and equalities committee last week.

Some committee members praised Stephenson and the EHRC for, they said, protecting single-sex spaces for women.

The guidance, which follows last year’s supreme court ruling that sex in the Equality Act refers only to biological sex, sets out that trans people should not be allowed to use facilities such as toilets and changing rooms for the gender they live as, and in some cases also for their biological sex. Instead, gender-neutral “third spaces” should be provided where possible.

But much of the hearing involved how the rules would work in practice. Kevin McKenna, a Labour MP who is a former nurse, questioned whether trans patients in hospitals could really be cared for in gender-neutral side rooms, given these are scarce and often needed for clinical reasons, such as for patients who are infectious.

In a statement after the hearing, McKenna said he feared the code “may not survive contact with reality”, adding: “This guidance is not ready, not practical, and not safe to implement. It will lead to terrible situations for trans people and their friends and families. It will not make life any safer for anyone else.”

Several MPs said they had been contacted by trans constituents who were particularly worried about the situation on hospital wards. “Several people have told me they are actively avoiding seeking medical care over fear of what ward they will be put on,” one backbencher said. “One trans man said he would rather die than be put on a women’s ward.”

Another Labour MP said they were also concerned at ways the code would work, particularly the idea that people should decide whether to challenge a person who appeared to be using a single-sex space not intended for them.

“Mary-Ann Stephenson kept talking about ‘common sense’,” the MP said. “You can’t operate that way because it’s completely subjective. Organisations will be worried they will be sued if they get it wrong.”

Another MP said the spread of names on the motion showed broad worry within Labour: “Looking at the list, it’s not just a mix of the left and right of Labour, but it’s people from surprising bits of the left and the right. The concern is really cutting through …

“The motion won’t change the law. The supreme court judgment will stand, unless there is legislative action. It’s about building momentum for the future, officially recording on the public record people’s opposition to this.”

Another Labour backbencher said that even after the government had worked with the EHRC to expand the guidance and include more practical examples, the situation felt unworkable.

“It doesn’t seem logical that we have introduced this system where we can challenge people on the way they look on whether or not they can use certain services. Because it’s so unclear what people should do, it feels like it has opened the door to a series of legal challenges.”

The 40-day period for the code to be laid before parliament ends early next month, after which it will become law in the coming weeks or months.

A government source defended the process, saying: “We understand that there are a lot of strong views on this, but we have tried very hard to make the guidance as workable as possible, and ensure it is legally robust, with as many examples as possible for service providers to follow. But it cannot cover every single legal eventuality.”