It must be very scary and hard for you, but you cannot bring your child up in a home of violent behaviour. There is plenty of help out there for you.
Like Izzy says, which area of London are you in? There are some lovely MN'ers out there who might be able to help you.
Legal Aid for divorce is ending in April and will only be available in cases of DV, so you should still qualify for it. Take a look at the following link for advice and help on finding a solicitor in your area.
www.divorceaid.co.uk/legal/legal-aid.htm
You would also qualify for free mediation, although they would not make you sit in a room with him due to DV, you would sit in separate rooms with one or two mediators, going between you to discuss child contact etc, although again, in cases of DV, I don't know how access is affected by that.
Do not feed trapped, do not feel like you have nothing, there are so many organisations out there that will help you and you will be able to get FREE legal advice to get away from him, so do not worry about that.
Stay strong, you CAN do this