Wulfyn is pretty much right here, but there seems to be a couple of re-curring issues on this forum regarding car insurance which no-one has covered.
1.Cancellation. You HAVE to do this in writing and return your certificate before your policy IS ACTUALLY cancelled. This is because technically the insurance company could still be liable to pay out if you hit someone, and can't prove the policy was cancelled. People will try anything when they're on the ropes, "no, I never called you, that must have been someone else etc. ", which is why an insurance co. has to be compliant. Usually, in cases of non payment, they will issue a written 7 day notice of cancellation by recorded delivery.
2.If you pay by DD there is often a 3rd party involved, the premium finance company. They pay the insurance up front to the insurance co. or the broker, and then collect the payments from you. If the insurance company or broker do not return any refunded premium to the premium finance people, then the debt is still outstanding with them, and it can take some time for the premium to go back to them. And it's not unknown for some parties to pocket the return, and leave the client debt with the premium finance co.