In 2018, Pink News commissioned a YouGov survey. They asked 1688 UK Adults four questions on 20th-21st June.
One question was:
“Do you think a person should or should not have to obtain a DOCTOR’S APPROVAL to change their legal gender on official documentation (e.g. birth certificate or passport).”
Only 18% said they should not.
It is already possible to get your sex on a passport changed with just a note written by a doctor – something that most people in the survey do not agree with.
Changes to the sex recorded on your birth certificate requires a diagnosis of gender dysphoria from a consultant (and other criteria). The UK government is currently consulting on whether this should be changed. Trans lobby groups want the process demedicalised with no doctors involved. This survey suggests the vast majority of the UK population are against this.