I'm not really sure but it might be worth looking into income support. I think if you claim income support you will automatically have the Child Support Agency managing the baby's father's contributions. I think you would then be eligible for housing benefit and other help. Please don't quote me on this though, it would be worth visiting either the Citizens Advice Bureau or your local jobcentre for further details.
If you did decide to go back to work you work be able to claim Working Tax Credit and means tested Child Tax Credit. I believe they also pay up to 70% of your childcare costs while you are working but again don't quote me on figures.
I haven't been in your situation though, sorry, so no real life advice to give.