Hi. If you get set up in a new home and then find yourself with no or a low income you can claim for Housing Benefit. There is a good site called 'entitled to' if you do a google search for it, and you can put in your details and it will tell you what things you can claim. You can also get child tax credits if you are a lone prent and not working.
I moved into a private rented house when I was pregnant with my then partner and a while later we claimed for housing benefit as our income went down, and when he left I was able to claim for things such as tax credits and for a short time Income Support when I was between jobs.
If you are not working and your youngest is under 7 you can claim Income Support.
As far as I am aware the only thing that might hinder you would be if you wanted to go to housing as a homeless person, if you have voluntarily left the home you live in now and then ask them to house you they can say no, as they might say you have intentionally made yourself homeless.
However this does not sound like your situation.
I would suggest going onto your local councils website for more local info and making an appointment with one of their benefits advisors, the other option is to go to Citizens Advice Bureau.
It IS doable if this is your decision, I have Housing Benefit to pay some of my rent as I work part time and I live in private rented.
I hope this helps.
Are you ok emotionally? Is this something you have wanted to do for a while? Have you talked to your husband about leaving, and what support he might be able to give you and the children? Or are you unable to do so right now?
Don't forget once you are set up in your new place you can contact the CSA for things such as child support.