So if you can't move out to a rented property in the UK, the other alternative is that you go back to the house you share with him and start divorce proceedings whilst living there.
Many couples have to divorce whilst living in the same house, for the exact same reason as you - they can't afford to move out.
So, get the divorce started. Meanwhile, you live "separated" in the house, like flatmates. In practice this means:
No more shared food or shared meals, have separate cupboards for food in the kitchen, divide up the shelves in the fridge.
No more doing each other's laundry or washing up after each other.
You move into a spare bedroom, or in with your DC on a mattress on the floor, or as a last resort onto the sofa to sleep.
You have a rota for cleaning "communal" areas of the house such as kitchen, bathroom and hallway. You don't clean the room where he sleeps. If at all possible, move all your clothes and stuff out of there and never go in there.
Separate your finances. You can keep joint names on household bills, but close any joint bank accounts, and make arrangements to split the bills. Consider taking your name off any bills you don't want, like TV services.
If you don't have enough money, you can claim benefits as a single parent and claim maintenance from him as the "main" parent whilst still living in the same house. Get advice from the CMS, the benefits office, Citizens Advice, or your solicitor.
Keep daily records, on your phone or in a notebook, of who does what for your DC - school pick-ups and drop-offs, who gets the DC meals, who takes them to clubs and activities, who buys clothes, etc. All of this will be evidence if he tries to claim he has been an equal parent (to get out of paying maintenance).