A poll shows that Penny Mordaunt, the minister for equalities, will have a tough time getting changes to the law approved by parliament

New rules allowing people to change gender without consulting a doctor are facing a barrage of backbench opposition, according to a poll of MPs that suggests ministers will have to rethink the plans.

A public consultation ends next week on reforms to the Gender Recognition Act that would allow people to legally self-declare as the opposite gender without needing to live in the role for two years and seek a doctor’s backing.

But the poll shows that Penny Mordaunt, the minister for equalities charged with introducing the changes, will have a tough time getting them approved by parliament and risks a bitter showdown with Conservative MPs, whose support she needs in a future Tory leadership contest.

The poll — one of a regular survey of