I think that they are referring to the results of this pol that YouGov did on behalf of Pink news, which showed the vast majority of respondents agreed with the statement that 'a person should be able to self identify as a gender different to the one they were born in.'
Which goes to show that people in the UK are pretty tolerant, and transphobia is exceptional rather than the norm. The British public does not want people to be discriminated against if they choose to dress unconventionally, and we aren't bothered if some people feel a compulsion to perform the stereotypes associated with gender.
What is very striking, and highly educational, is how they have focused on the response to the initial vague statement, and pointedly ignored the responses showing that nobody is in favour of the kind of self id they have been lobbying so hard to push into law, beneath the radar of public awareness.
If you look at the answers to statements about the process of legal gender recognition, you will see that only 2 of the 12 categories of people polled in the UK were in favour of making it easier for people to legally change their sex (just 18-24yr olds and people who say they vote Labour), and none of the 12 groups was overwhelmingly in favour of allowing them to do so without a doctor's approval and having spent 2 years as their preferred gender.
So when transgenderists claim "On 14th June 2020, the Sunday Times reported that, despite 70% of responses to the recent consultation on the reform of the Gender Recognition Act being in favour of self-identification, the UK Government intends to scrap the GRA reform and roll back the hard-won rights of trans and non-binary people" they are being exceedingly disingenuous.
The majority don't give a toss about people choosing their own preferred gender and performing the related stereotypes, but they are firmly against the proposed changes to the gender recognition act that Stonewall, pink news and the rest of the trans lobby are still pushing for, and in completely in favour of the governments decision to scrap the proposed reforms.
Have a look at the results for a quick masterclass in lies, damn lies and statistics.
Notice too how nobody thinks it is fair to allow males to compete in female sports, and how the question about allowing transwomen in women's changing rooms doesn't mention genitals. I can't remember which women's group it was that paid for an independent poll of UK attitudes a while back, but do remember, very clearly, how the number of people in favour of transwomen in women's sex segregated spaces plummeted once the concept of female penis was explained.
Download and save the graphic. You too might find it comes in handy at a later date when you need to shed light on what the British public really thinks, compared to what the Stonewall and Pink news propaganda machine wants you to think that they think.