You should be able to get a refund. Outline exactly whatn happened, dates of direct debits, copies of policies in a letter.Get a letter from the company you changed to stating that you were insured with them from 06 to 07.
If you were with the insurance co in question from 05 to 06 and paid by direct debit they will automatically renew your insurance every year until you tell them otherwise. I assume in 06 you changed companies and did not notify them?
So as far as they were concerned the letter they sent you this year was your renewal as they did not know you went elsewhere.
Depending on the company they should accept it as aa misunderstanding and refund you.
Moral of the story....ring your insurance co if you are going elsewhere. It's common courtesy and will save headaches.