Complex issue benefits and non uk citizen though child is

I am on tourist visa and have had a child with UK citizen, which makes child British too. I know i am not able to get public funds and my query is that I am currently living with the father and our child who is 5 and he is threatening me and i need to leave with my daughter but we have no money so we are stuck with her dad and in this scenario. Because child is UK citizen will the council help us to get somewhere to live and will we be supported by the benefit system if we leave? really have no idea where to turn.

PK