I think private renting may be your only hope unless you can make some adaptions to your house, personally I would put bunk beds in both rooms, everyone will moan but will get used to them, then I would look at renting privately, the council are not going to help you, they have bu$$er all properties available as it is and most have huge waiting lists.
renting privately is not always as expensive as you think, check out rightmove.com and look at all the available options open to you. my neighbour bought a caravan and parked it on the driveway to create a bedroom for himself, you could also utilise the living room by buying a bed/settee
although we read about people on benefits living in mantions in knightsbridge rent free, it is not common and there is not a lot of available social property.