However, since she was born he hasn’t been a great partner. He is openly hostile towards me, is no longer at all loving, doesn’t attend any family engagements on my side of the family, however he expects me to play the part of his partner without having to make any effort for me at all.
So leave him then. It's really not a difficult decision to make. He's a dickhead. Kick him out and get a job. Claim UC until you find a job that pays enough not to be eligible for it.
If you can't sort out child access arrangements amicably, he'll have to go to court for access then, won't he. Put in a child maintenance claim ASAP, like the same day he moves out.
I am assuming you're renting. Contact the landlord if it's in your sole name, explain you've split up and ask permission to change the locks (at your expense). If he's on the tenancy tell the landlord you've split and want to continue living there (if you can afford it). If you can't afford to keep living there then give notice and get looking for something you can afford.
Contact the council If you're going to be homeless. With a child you'll be priority. You won't be if she goes to live primarily with her father, because he'd then become the resident parent. In that circumstance you'd just be a single homeless person eligible for a one bedroom flat (as permanent) and a room in a b&b or hostel (as temporary).
If you own the home jointly he'll be allowed to live there, so get the property valued and get it up for sale ASAP. Separate from him properly even while in the same house. No sharing a bed, no doing his laundry or cooking, no giving him lifts in your car or letting him drive it, no doing joint food shops with him or for him, no shared bank accounts, no tidying away his stuff or washing up his dishes, no doing him favours or asking him for favours. Put in a UC claim as a single mother, claim child benefit too if you're not already doing that and claim child maintenance from him.
If you own the home you can just kick him out without any notice. Or just change the locks while he's out and refuse to let him back in, if you think he'll be aggressive in any way at being asked to leave. "Asked" is polite, you're not actually asking him, you're telling him and he has no choice in the matter if it's your home and not jointly owned. You wouldn't have to give him time to find somewhere else, where he goes is not your problem.