DP did that with his ex for a year whilst they sorted out the divorce and she looked for a new place. From what he tells me it was very stressful for everyone involved and not really to be recommended. His ex had found new bloke who was staying over... Might be worth it for a short time whilst one or other of you looks for a new home.
Re benefits - if you are not married, you can in theory claim them as a lone parent, even if you're in the same house, though you'd need to convince the benefits agency that you've separated. Probably OK as long as you have a spare room or somewhere to move into. If your youngest DC is under 5 you can claim income support, otherwise JSA - which means you need to be looking for work. Both are means tested and you won't get anything if you have over a certain amount in savings (£16,000?). You can get child tax credit though separately which is not means tested. If you move out, you can claim housing benefit to help you pay the rent, and possibly you could beforehand depending who's on the tenancy - I'd get advice from CAB or someone on that one.