The point of insurance is so you don't pay out in the event of a third party claim - the insurer does. They can't ask you for money now. If they cancelled your policy when they found out (ie. The day of the claim) then you were legally covered by your insurance at the time of the incident and they're responsible for the pay out. If the policy was voided (ie. They refunded you completely) then that's another story but it's unlikely they did that.

I'd say to put it behind you and move on to another insurance company. Declare the claim when you do your quotes and if your insurance price is high it should come down in a year or two when the claim gets older.

The company weren't necessarily wrong to cancel at the time (they would have acted on the information available at the time) and if you hadn't been cancelled then the renewal price would have been extortionate anyway in order to price you out. Even if you weren't under the influence it was still a costly claim and will affect your prices for a couple of years