Before you sell your car, try getting a quote for putting one of your parents on your own policy as an additional driver for your car. Doing it that way round - rather than getting a parent to insure your car with you as a named driver (which can result in a prison sentence!)- is entirely legal (even if the parent will never actually drive your car) and, somewhat strangely, can often result in a substantial reduction in your premium.
Also check out different classes of insurance. '3rd party only' (or '3rd party, fire and theft') isn't always the cheapest. Sometimes 'fully comp' can be significantly cheaper. (That's not written as 'pure theory'. My own policy is 'fully comp' because it was much cheaper than the alternatives!).
Chris