I found this while looking at some YouGov polls. This is from 2020.

https://yougov.co.uk/topics/politics/articles-reports/2020/0...

Overall it concludes - Britons support the right of transgender people to use facilities for their chosen gender, but oppose making the legal transition process easier

50% to 27% Britons believe that people should be allowed to self-identify as a gender different to the one they were assigned at birth.

Across the survey two distinct groups of opinion emerged, based on politics, gender and age. Labour, Lib Dem and Remain voters, along with women and younger people, are likelier to hold more trans-friendly views than Conservative and Leave voters, men and older people.

Young Britons – those aged 18-24 – are most likely to accept the new gender identity of transgender men and women, at 54%. So too do a majority of Labour voters (53%). Least likely to recognise that transgender people now hold a new gender status are Leave voters (32%), men (33%) and Conservative voters (34%).

Men and women hold opposing views on the issue. Almost half (47-49%) of women accept the new gender identity of transgender men and women, while about three in ten (29-30%) do not.

By contrast, men refuse to accept the new gender identities of transgender men and women by 43% to 33%.

When it comes to sports, however, Britons are much less supportive of access for trans people. People tend to think that transgender people should not be able to participate in sporting events for their new gender, but noticeably more so when it comes to transgender women (55%) than transgender men (44%).

63% think a doctor’s approval should be required compared to 16% who think it is unnecessary.
61% to 16% that a transgender person should have to provide evidence that they have been living as their new gender for two years before being legally entitled to change gender.

People tend to be fine with transgender people using facilities for their new gender, but not if they have not undergone gender reassignment surgery

Despite being such a prominent battleground in the trans-rights debate, Britons tend to support transgender people using their new gender’s toilet (46-49% vs 28-30% opposed) and changing rooms (42-45% vs 32-34% opposed).

Women tend to reject the argument that allowing transgender women to use female facilities puts them at risk. By 46% to 28% women say that doing so does not present any genuine risk of harm. Men are more sceptical, thinking such a move puts women in danger by 31% to 37%. Among the overall population 39% believe there to be no genuine risk compared to 32% who disagree.

It is worth noting, however, that Britons do not support such access for those who have not yet undergone gender reassignment surgery. By 41-46% to 26-30% people oppose those who have not physically transitioned being able to use their new gender’s changing rooms. Likewise, 39-41% oppose them being able to use their new gender’s toilets, compared to 31-32% who are in support.

People also tend to believe transgender women who have been victims of assault or rape should have access to women’s refuges (47% vs 26%).