Firstly, your GP may be misinformed or working to old standards. NHS guidelines changed last August, and it is now possible for your GP to put you on HRT before you go to CHX. Have a look at the
current protocols for England (in fact, I recommend printing these out and taking them to your GP); page 17 discusses 'bridging endocrine treatment', which is what you should ask your GP for if you want to use T as soon as possible.
Secondly, I hate to break this to you, but CHX may not put you back on T until they've completed their mandatory minimum 3 months of assessments. I hope you're lucky though: they do seem to be starting to use the new protocols, but there are people here who've waited a long time to get their hormones. Anyway, if your GP won't prescrible bridging endocrine treatment, take all the documentation of your previous prescription with you to CHX and ask them to give you bridging treatment whilst you wait to complete your assessments.
Lastly, whenever I'm misgendered, I throw it back in the face of whoever decided to presume my gender for me. I try to do this gently and with humour wherever possible... but I always start by thinking of how a cisguy would react if somebody called him 'madam', and I respond accordingly. For example, I've been known to look shocked and embarrassed, then I look down towards my crotch with exaggerated worry and say 'Madam? I bloody well hope not!'. I then joke about needing to go to the bathroom to check nothing's missing.
Of course, I know there's nothing there in the first place to go missing. But a cisguy
would say that sort of thing, and joking about it defuses he situation and makes me feel a million times better. And if the person who called me 'madam' feels a bit embarrassed, that's unfortunate... but they shouldn't presume people's gender if they don't want to feel embarrassed when they get it wrong.