Paperview - I am assuming you have a child/ren and got into the private rent sector because the LA had no housing available - is that right? Because as a mother with dependent children you are in priority need and it is the duty of the LA to ensure that you are housed. I know of course that you also have MH problems - you must feel like you are in the middle of a nightmare.
I think you need to contact the Housing Dept asap and advise them that you are going to be homeless with children when this tenancy ends. They will probably tell you to find a private rent and a lot of landlords don't take people on Housing Benefit but I think that is changing a fair bit these days as they know they will get their rent paid by HB. The LA can loan you the 4 weeks advance rent and deposit that will be needed for a private rent and this fulfills their duty to you as a homeless person in priority need. They might not tell you that but they can (have done it for my step gr dgtr 3 times!)
The other people you need to contact are CAB as they have good advice on housing matters. It is best to make an appt because sometimes they have lawyers in housing law who do sessions for them, or someone who is very experienced in these matters.
The other people are Shelter and they are an organisation specifically for housing matters including homelessness. They will advise you of your rights and will sometimes attend meetings at the Housing Dept with you. You can find your nearest Shelter by googling and it might be some distance away but you can still contact them by phone or email.
If there are no private rents available in your area, the LA should put you in temporary accommodation until one comes available. Some LAs have lists of landlords willing to let to people on HB. Afraid it differs greatly between different parts of the country. Are you willing to say where you are, if not don't worry, it's just that the inner city areas are going to be inundated with homeless people and so you might find it more difficult. One thing is you are not going to be left on the street with your child/ren. Do you have any RL support - I do hope so.
When you google Shelter, have a look at the site as there is a wealth of info on there and housing law and what rights people have etc.
Happy to help further if I possibly can.
There is a lawyer on here (Madmouse) but don't think housing law is her specialism, but it might be worth putting out a call for her.