This is a typical example of how the authorities in the UK have no interest in sorting out problems that are of their own making. You are making things worse by acceding to their demands.
In your situation, once I had written to inform them of the situation � I would, in no uncertain terms tell them to f*ck off. If they wanted any money, I would see them in court (with a copy of the letters I had written to them).
How can you license a car you do not own and have no insurance for?
Soon you will be receiving parking fines, speeding tickets and maybe the congestion tax in London for your old car. If you keep paying, they will keep asking.
Whenever dealing with any governmental organisation � assume that the people you are dealing with are complete d*ck heads and you won�t go far wrong.
Always keep a copy of any documents sent � preferably send copies/keep originals.