I always find it a good idea to make sure of your facts before you confidently make assertions, otherwise you look a little foolish @SmallCalpolFiend - your assertions are in bold
Stonewall don't classify anyone who cross-dresses as trans
From the Stonewell website:
Trans people may describe themselves using one or more of a wide variety of terms, including (but not limited to) transgender, cross dresser, non-binary, gender queer.
Trans groups aren't lobbying to remove female-only spaces
Stonewall, Gendered Intelligence and Scottish Trans Alliance all submitted evidence to the GRA consultation doing precisely that. Collated evidence is here:
https://womansplaceuk.org/references-to-removal-of-single-sex-exemptions/
Or of course it's all visible on the U.K. parliament website.
It's not that easy for children to get medical help to transition, or even delay puberty
Before 2011, puberty blockers were only given to over 16s in the U.K.. Since then the age has lowered and lowered, with the youngest child being 11. Transgender treatment: Puberty blockers study under investigation www.bbc.co.uk/news/health-49036145
This is despite evidence that children have increased suicidal thoughts. Over 1000 children in the U.K. have now been prescribed blockers.
Your turn backing up the other assertions you made!