Refund. Policy Terminated

I’m absolutely disappointed in the service. On the 20th of May I was debited my premium and in fact it was not a debit date I had registered. Called in and enquired and they advised why they did they I then asked for a termination as intact yes iv been meaning to go back to my old car insurance. The guy confirmed my termination and sent me details via email. I then joined with my new insurance and advised them since I was already debited I was going to have cover until the 20 June so my new cover the other side should start as of 20 June. But nooooooo Miway has now debited a premium when I have cancelled my policy. What should happen with my new insurance.

A refund please.