OP I don't think you're reading the replies properly - probably because you are tired and poorly and desperate 
What people are saying is that the council housing rules arent fair in this situation, and you have to be very careful that you don't by accident get yourself classed as having made yourself 'intentionally homeless'
So, moving out at the end of the contract because you can't pay the rent is really not a good idea, as you will be classed as making yourself intentionally homeless.
I know it's not right and you don't want anyone to be out of pocket... And I'm sure there are ways round this, but the most obvious thing (to move out) is not one of those ways.
Now, practically:
- are you known to the council as a disabled / chronically ill person? Ie have you had carers in the past? Or an assessment?
- do you get dla?
- do you get disability / sickness benefits for not being able to work? (sorry can't remember the name, I'm tired too!)
- are you on the housing register? As a disabled person?
The reason I'm asking all this is that any of these things helps give the picture of your need to the council.
You need to fill in a housing form BUT because you are chronically ill and in danger of becoming homeless, and you have a child... You need to talk to adult social services too.
To get evidence of this awful situation you're in, you'll need a letter/ support from adult social services and/ or your gp to explain how ill you are, any special needs for your living (eg no steps, somewhere to store wheelchair/ equipment etc) and the occupational health person in adult ss will help assess this with you. This evidence, plus your imminent homelessness will get you put as a priority for housing.
In my area, if you're disabled and in an unsuitable home, you are immediately classed as band B, if you become homeless you'll get raised to an A, which is the highest priority. They will house you in a hostel or somewhere as an emergency but it's likely to be unsuitable for you depending on your illness. So they'll be looking to get you into better housing urgently, and adult ss should help with things like carers and help packing if they've assessed you as needing this.
So here's an action plan (in my opinion so not The Law!):
- Get advice on current housing situation (ie to avoid making yourself unintentionally homeless by accident)
- Phone housing department and ask them for help. Emphasis your chronic illness and your child. Ask them to help you get to see adult social services for an urgent assessment. They may not be able to do that, which takes you onto step 3.
- Get appointment with GP, tell them your not coping, you're likely to become homeless and you are ill. Ask them to refer you urgently to adult social services (they can do this). Also ask for a letter to support your housing claim on the basis of your illness, ask them to include the effect of homelessness and temporary accommodation on your illness and ability to function.
- Tell adult social services very honestly about all the problems you have. They will need to do a thorough assessment of your needs. They may suggest alot of different stuff but the main thing you need them to do is help you work out your needs in your next accomodation and the OH will wrote to support your housing application.
- Either via the housing service OR adult ss, you may be directed to a charity/ trust/ outside agency will helps disabled people fill in their housing forms and deal with the process.
I know it looks like loads to do but you need to start on it, as everything is so slow and you don't have time to waste.
I'm sorry this is happening 