Dear Mehdi's mum, just read your OP and am close to tears.
There is something better out there for you, please believe that!
It sounds like you are deeply unhappy and lonely, your Dh sounds like a liability to yourself and your DC not a help in any way. These situations are never 100% cut and dried I know as no-one is 100% bad and of course he is the father of your child.
That said, it seems from what you have said that if you could solve the housing /childcare problems you would wish to leave him.
I am no expert but if your DH has physically assaulted you then surely there are leagl avenues you could go down?
If this is not an option, if you work more that 16 hours per week then you can working and childcare tax credits, if your Dh is not giving you any money you will UNDOUBTABLY be better off doing this as a single parent. Like another poster has said, tax credits will pay up to 80% of childcare and it doesnt have to be a nursery (although I think there are some night /24hr ones around so maybe that would be an option?) it could be a childminder, there are some advertised in my are (SW) who will do overnight/evening care so surely in London there would be similar.
Obviously to get the tax credits as a single person then you would need to split from your partner in terms of accomodation. I was not 100% sure of the arrangement, ie do you have a joint tenancy or do you have seperate addresses but just from the same c ompany?
failing all else, could you quietly save up a little money each week with a view to relocating, could the company relocate you to a similiar position elsewhere?
There's got to be ways to improve your situation, please let us know how things are going.
best of luck