Doesn't Britain still have Islamic migrants in their country? If THEY begin to speak out against them, oh boy...
Muslims in the UK are mostly South Asian, where there is a traditional third gender for male homosexuals, called hijras, who are more or less tolerated, so Muslim Brits tend to be sort of accepting of trannies (if the end result is "straight"). It's similar to the situation in Iran, where there's a death penalty for homosexuality, but the state pays for sex change operations. There's a famous Brit FTM with a YouTube channel who goes by Jammidodger. She obviously transitioned due to internal and external homophobia. Her long-term girlfriend is from a South Asian background (don't remember if Hindu, Sikh or Muslim, but the attitudes to hijras are similar, regardless) and, pre-transition, they had to present as "just friends" to the GF's SA family. Once Jammidodger transitioned, the SA family accepted them as a hetero couple.
South Asian Muslims generally tend to think that being a good Muslim is only about how you behave publicly. What you do privately is your own business. So if a man has a wife and children, but likes having sex with other men, that's fine, as long as he keeps it secret, but if he publicly stated he was gay and married a man, that would be very haram.
ETA: That being said, hijras are definitely not considered to be the same as biological females, so legally treating them as such might not go over well with these sorts of traditional South Asian Muslims. However, this mostly effects women participating in the public realm (i.e. sports), or needing protection from predatory males (shelters, jails), and traditional Muslims generally are not that enthusiastic about women's rights, so they probably wouldn't care. The idea that being a good man means protecting women and girls is not really part of South Asian culture.