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Do you need it?
The law doesn't make you insure a Class 2 or Class 3 mobility scooter. GOV.UK recommends it, and the reason is liability. In 2023, collisions involving mobility scooters in Great Britain left 17 people dead, 94 seriously injured and 229 slightly injured (Department for Transport). If you're found responsible for an injury, the claim is against you personally.
Some people are already covered. A Motability lease includes insurance and breakdown assistance. Home insurance can sometimes cover a pavement scooter, but Age Co and Saga both exclude scooters registered for road use.