Leaving it until the airport
Cancellation cover starts the day you buy, so buy as soon as you book, not the week you fly. It matters even more than it sounds: many insurers will not cover you at all once your trip has already started, so you have to buy before you leave home.
Not declaring a medical condition
Skipping a pre-existing condition to save a few pounds can void your entire medical claim, not just the part relating to that condition. Always declare, it is the single biggest cause of rejected claims.
Assuming a GHIC is enough
The free health card helps inside the EU, but it will not fly you home or cover private treatment, and it does nothing for cancellation or lost belongings. It is a top-up to insurance, not a replacement.
Ignoring FCDO advice
Travel to an area the FCDO advises against and a standard policy can be void entirely, including for something with no connection to the reason for the warning. Check the advice before you go, and if you do need to travel somewhere high-risk, look for insurers that specialise in covering those destinations.
Focusing on baggage, not the big stuff
A lost bag is annoying; an air ambulance is ruinous. Make sure the medical and repatriation limits are high, ideally a million pounds or more, before you worry about luggage.
Not checking the exclusions
Scooters, skiing, hiking and alcohol-related incidents are often excluded as standard. Add cover for what you will actually do on the trip.