Several questions that matter here
Who owns the house and by how much, is it 50/50 or in his name? Is it rented as that's a whole other ball game.
Do not give up work. The whole speel if you'll spend all your money on childcare is not true, if your in a low paid job you still get 20% tax free childcare and childminders can cost £4 an hour, that's BEFORE the 20% back.
Even if you go back part time, do not give up your job. You can't just jump straight back once the child gets to school, it dosnt work like that. Plus your putting yourself back 4 years in terms of yearly increases in salary for time served, never mind promotions.
Ultimately you need your own money.
Even if you got married and he left you, you would struggle, if not find it impossible to run a house on benefits. Even if he pays the mortgage through CMS, which he is legally made to do wether your married or not.
I have one friend who's husband left her, and she had gave up work. And another who's boyfriend left her; but she worked. And I'm putting it out there that the friend who worked was 100% fine. The married one ended up taking him back as should couldn't afford the bills and struggled to find work. Both had DC.
Giving up your job is giving up your independence and opportunity to make your own choices. Don't do it.