Hi. Mumsnet's resident trans widow guidance poster here.
There is no such thing as "used to be a cross dresser", they either continue to do it in secret or they have binge and purge cycles. It won't have been for a laugh, it will have been for sexual reasons. He doesn't have gender dysphoria, he is an autogynephile, ie he gets aroused by himself pretending to be a woman,
Men in this situation getting their child to call them Mum is not unusual, there is a whole thread about it on FWR. Unfortunately I don't think that this in isolation would be of concern to social services (although I'd be happy to be proved wrong).
However putting that aside, (and I 100% understand why that issue feels like the worst thing), you are in a physically and mentally abusive relationship. He is gaslighting you.
You need to live separately ASAP. As others have said, speak to women's aide about getting him out of your property. Are you able to throw his stuff out and change the locks?
Find out what benefits you would be entitled to. As a single parent there's every chance you'd be able to get benefits to cover your rent.
Once you are living separately his opportunities for LARPing as Mum will be vastly reduced and there's every chance he'll lose interest in your child. This is the best way to resolve the situation.
Tell your friends and family about the abuse. You don't necessarily have to mention the appropriation of motherhood just yet if don't want to. The other stuff is bad enough on its own.