I'm sorry but where did you get your figure of "hundreds of thousands." Statistics from the ONS reporting on results from the 2021 census show only 96,000 individuals identifying as trans.
The census question on gender identity was a voluntary question asked of those aged 16 years and over. The question asked “Is the gender you identify with the same as your sex registered at birth?”.
Overall, 45.7 million (94.0% of the population aged 16 years and over) answered the question.
The remaining 2.9 million (6.0%) did not answer the question.
In total of 45.4 million (93.5%) answered “Yes”, indicating that their gender identity was the same as their sex registered at birth.
A total of 262,000 people (0.5%) answered “No”, indicating that their gender identity was different from their sex registered at birth.
Within this group:
118,000 (0.24%) answered “No” but did not provide a write-in response
48,000 (0.10%) identified as a trans man
48,000 (0.10%) identified as a trans woman
30,000 (0.06%) identified as non-binary
18,000 (0.04%) wrote in a different gender identity