Scarlett// My flat has been interest only- it's worth nothing. //
Struggling to understand what you mean here. You have a property bought on an interest only mortgage. This means, either you were going to sell it at the end of the Mortgage term, to pay the Capitol off, or have an Assurance policy that matures at the end of your mortgage to pay off the Capital. Whichever you have its not 'worth nothing'. I doubt you will get a council house if you already have a property.
So, my advice would be to get your Mortgaged property valued -you may find out it has gained substantial value over the years, and you may have a tidy sum left after selling and paying off the Capital owed on the Mortgage.
Short term, speak with your Landlord and ask that instead of eviction, you can extend your Tenancy on a rolling monthly Tenancy, which will mean if they do sell the house quickly (unlikely) the house will have vacant possession on Completion of sale. ( it can take up to four months minimum from accepting an offer to Complete)