Limited leave to remain and Benefits

I am on discretionary limited leave to remain granted due for extension in 2 months time.I was granted on the grounds that i live with my british partner and our child. We now have 2 children and my partner has been abusive towards me.He has even been arrested once and charged to court for assaulting me physically.
I want to leave him now as a result of the domestic abuse but council wouldnt accommodate or give me housing benefit because of my status meanwhile my visa does not say 'No recourse to public funds'. Social services will only accommodate me if i agree to move outside London,i have a child with extra needs so its difficult for me to move as getting another school with the right support for my child is almost impossible.
What do i do as the environment is not condusive for me and the kids?
Bolly

I'm sorry to hear that. You can claim public funds under DLR. the social worker has a legal duty to ensure the welfare of the child. They should not be threatening you, speak to the manager and explain you'll get your MP involved. The council must give you housing benefit as you're entitled to it, again speak to a manager.