If you manage to get a private rent, you can certainly claim housing benefit, although you may have to find the deposit yourself, usually about a month`s rent,and reclaimable if you leave the property in the same state as when you move in.
You would probably get the full rent, as long as you don`t go over the top with the size of house etc. Which in your case would mean two bedrooms, as small children can share a room.
In some towns you can even get help with the deposit.
I agree with k8bailey, a good idea to see someone at citizens advice, if they can`t help they will put you in touch with someone who can.
They will also advise about other benefits that you can claim.