Way back in 2004, the Labour Party introduced the Gender Recognition Act to make it possible under strictly limited circumstances for individuals to apply to have their birth certificates reissued showing the opposite to their birth sex.
The debate on the GRA was not very long or detailed. A number of MPs and Lords did try to raise exactly the issues that a lot of people on MN are raising now. They were all told not to worry, it was only ever going to affect a tiny number of people (5000 was the estimate) and there would be very strict gatekeeping.
Only over 18s could apply. Medical confirmation of a gender dysphoria diagnosis needed. Assumption (but not requirement) that anyone applying would be likely to be having medical treatment, e.g. hormone therapy and/or surgery. Anyone married applying for a GRC would have to get their spouse's agreement. Nobody could apply until they had been living in the target gender/sex for two years minimum, proof required.
Fast forward to now and there have indeed only been about 5000 Gender Recognition Certificates issued in that 14 year period. However, Stonewall and other transgender lobbying organisations/individuals now say that the number should be far higher. They cite the cost (which is £70, with discounts for people on a low income), the intrusion and bureaucracy (which is not that different from having an interview to get a passport or benefits) and they want the age limit reduced and no necessity to have a diagnosis of gender dysphoria. They don't want any evidence to be required of living as the opposite gender/sex for any period of time. They also want the spouse to have no say at all.
Stonewall have a definition of transgender that would include most of the population. A conservative estimate of everybody who might identify as transgender or nonbinary or genderfluid in the UK at the moment is half a million.
That's a bit different from 5000 people with agonising gender dysphoria seeking medical treatment as an absolute last resort.