I've been to FTM London a few times. It's a very friendly group; they let you mix first, then you usually sit in a group where you discuss the topic of that month; then you have a chance to go to a pub afterwards. For me though I find the group a bit too big so it's difficult to start talking to people. But there is a library for you to borrow books as well as them handing out secondhand binders.
There's also TAGS swimming group which is a swimming group for trans people; although I haven't been. There's also the Spectrum support group and London Friend; although I haven't been to those either.
If you have time and want to get a haircut I go to Barberette in Hackney which is a queer barbers. There's also Open Barbers; another queer barbers; which is more popular with trans masculine people.
Not sure if this will help but there's a new fb group called Non binary London as well.
Hope this was helpful
