Under my insurance, I can drive another car (only third party cover) so long as the other car is insured. If the other car is not insured I would not be covered. If I transfer my insurance, my car will not be insured.
I had a similar situation a while back, my insurance company said that I could keep the old car insured for a week free, but after that it would be something like €80 per week, a rip off!.
Contact your broker to se what the story is, I was fortunate to sell the car in the "free" week, ie the first week.