Hi Sensei.
If you only keep the car for a month after taxing it, I guess you lose 5 months as there is no keeper for the tax to be refunded to.
However, if you pay monthly by direct debit for the tax as this is now a new option, then as soon as you sell the car, a new owner is registered and you stop paying. Maybe this is the solution?
I will try it and report back
If anybody else has any information please feel free to chip in.
Many thanks.