separating and need urgent advice

Hoping someone can help as I don't know where to start. My husband and I have agreed to separate after years of arguing and not getting along. We believe it would be much better for our children for us to live separately and I'm confident that we will come to an amicable custody arrangement. Our big problem is that we are in negative equity and cannot sell our house. My husband is refusing to leave as he has always paid the mortgage and can't afford to continue to do so and also provide for himself and I totally understand this. We are in arrears and haven't been able to make full repayments for over 2 years so he is currently paying interest only payments and struggling at that. I work part time and earn 290 a week. My question is if myself and my 2 children were to move out of the family home would I have any entitlements. Rent allowance? FIS? One parent family allowance? I'm not looking for handouts. I genuinely cannot continue to live under the same roof as my husband. My mental health is suffering and it's a toxic environment for my children to be growing up in. It would also provide some form of stability for them to be able to still visit and stay in the family home they have known all their lives. Eventually when the market picks up we would hope to sell and move on to two smaller properties. Idealistic maybe but I can't see a way out of this at the minute and desperately need advice. I just want to move on with my life. At the minute I feel so trapped and depressed and also extremely guilty as it was me who asked for the separation. All advice appreciated thank you.

I can't answer the welfare question, but you should put the mortgage question in the "mortgage arrears and negative equity" forum or maybe the "problems with joint mortgages forum". Use the Case Study format and you might get some avenues to explore.

You can apply for Family Income Supplement after you move.
You may be entitled to apply for One Parent Family payment, it depends on the age of your youngest child (must be under 10).
If your husband is working, then you should also seek maintenance.

Rent Supplement will be a bit more difficult to get.
You must have been renting privately (and have been able to afford the rent) for 6 of the previous 12 months, or you must have been assessed by the local authority as having a housing need and be on the housing list. There may be difficulties getting onto the housing list while you are still joint owner of the family home.
Rent Supplement is a means-tested payment, your wages and any other SW support will be assessed.