Wait, what? So he runs, abandoning you and the child and now he turns around and wants to fight you for custody after saying he didn't want anything to do with the child? After you've been through hell and back trying to keep your child, the child that you alone have been carrying without his support? And those idiotic social workers think this is alright just because you are trans? Pardon my language but what they're pulling here is complete and undeniably bull->-bleeped-<-!
........I just looked up UK anti-discrimination laws, I saw a comment about transsexuals being covered in those laws but sadly I cannot find many details about it and to what extent trans people are protected by those laws, sorry, I tried to see if I can find something to help you but I don't really know what to look for to get the specifics. However, if you have your sisters willing to take in the child, are they also willing to help you raise the child if they stay with you? Having family there who's willing and capable, as well as able to clear their 'requirements' for keeping the child there to help you can hold a good bit of sway in some cases, though that depends on the judge you get. But if they're trying to pull you being an alcoholic, they're just looking for any reason to take the child from you, possible they may even be making things up too, underhanded sons of. . .