I successfully put in a claim a few years back when I buckled an alloy in Cambridgeshire. They required me to fill in a claim form, time and date of incident, photograph of the damage and a copy of the quote to repair. They paid out in full without too much of a quibble.
If the pothole has white markings around it, indicating they are aware of its presence and intend to repair it, then it can be more tricky. But I know people who’s be successfully claimed part-payment in such circumstances.