Well the 2020 poll is quite helpful in this regard.
A person should be able to self ID as the gender they identify as: strong yes. (This appears to have now completely reversed.)
A transgender woman is a woman: weak yes.
A transgender man is a man: weak yes.
It should be made easier for people to change their legal gender: strong no. (Note that this contradicts question one, because self ID is about making it easier to change your legal gender. This suggests that in 2020 most people did not understand what self ID was and may have assumed it meant changing your pronouns or something.)
Transgender people should be able to change their legal gender without the involvement of their doctor: Unambiguous no. No group agreed with this.
Transgender people should not have to provide evidence that they have been living in their preferred gender for at least two years: Also unambiguous no.
Transgender women should be allowed to take part in women's sporting events: Nope, nope, nopity nope. Again, no group, not even 18-24 year olds or Labour voters agreed with this.
Then we get on to single sex spaces and this is where it gets really interesting.
All groups agreed that trans women should be allowed to access women's refuges if they are a victim themselves and most groups agreed that trans people should be allowed to use toilets and changing rooms for the opposite sex.
However, when the follow up question was asked, specifying that the trans person in question had not undergone any gender reassignment surgery, a lot of people changed their answers and overall a majority of respondents disagreed that they should be allowed to use toilets and changing rooms for the opposite sex.
Now, there are some flaws with this survey.
First of all, it is not at all clear to me whether all respondents understood that a trans woman is a biological male and a trans man is a biological female. This really needs to be made crystal clear in any polling.
Secondly, it shows how undeveloped most people's thinking was about these issues at the time. It doesn't make any sense that people said they were strongly in favour of self ID but strongly opposed to making it easier for people to change their legal gender, because these two things are the same. It also doesn't make any sense to say that trans people who have had gender reassignment surgery should be allowed to use toilets and changing rooms for the opposite sex but that those who haven't should not, since we have no way of knowing who has had gender reassignment surgery and who has not.
What it does show is that even in 2020 the general public was already quite "terfy" once you cut through all the be kind crap, and we know that that trend has only continued. Whether that is due to increased awareness of what these things actually mean or recent events giving trans people a bad reputation, or a combination of both, I don't know.