I'm not trans or an immigrant - so please feel free to ignore my thoughts on the matter.

Anyway, regardless, it's a good question, but probably not one with an easy answer - I think in this case, the best option might be to ask the people who make some of those decisions - in theory, if you look at the webpage gov.uk Apply for a Gender Recognition Certificate, there's a few email addresses and phone numbers that may be able to answer half of the question - though separately you may need to speak to the immigration/visa people gov.uk partner/spouse visa for the other half of the question. All in all, you've got a few layers of complexity here.

My own experience with contacting other government departments on different things is "very slow to respond, but then surprisingly helpful in the end".

There may be some useful advice on websites such as transactual.org.uk or transinformed.co.uk - your specific situation isn't likely to crop up in a FAQ, but you may be able to pick up half an answer to start with - then there are contact details on there which would hopefully lead to some useful information.

Sorry there's no clear and immediate answer I can find.

I wish you the best of luck!