If you're looking for an LGBT friendly city, Brighton's great. It has two unis (Uni of Brighton and Uni of Sussex), so you have options. I've heard good things about Manchester too (I think there's 2 unis in Manchester too), but I've never been so idk for sure. London's pretty good too, but obviously London's very big and there are some not great areas, so be sure to check. There's lots of unis in London though, so you have lots of options.
My advice would be to ask at open days about attitudes towards LGBT people both within the uni and in the local town/city. I didn't do that initially and I got outed several times and have now dropped out. I'm reapplying this year and checking what it's like for LGBT students at all the unis I've applied to.