However this is likely to change very soon since COVID-19 - there is "urgent legislation" on e-scooter rental trials going on: https://www.gov.uk/government/consultations/legalising-renta...
Infuriatingly, privately owned e-scooters will remain illegal even if rental fleets are legal. I do not understand why it would be legal to drive a rented e-scooter, but illegal to drive a privately owned e-scooter :-/