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UK law is not fine with electric scooters. Anything with a motor (except for certain vehicles used by people with mobility difficulties: https://www.gov.uk/mobility-scooters-and-powered-wheelchairs-rules) requires a licence to be used in the public realm. I'm sure some people can ride these scooters when they buy them, but you're still putting someone in charge of quite a fast vehicle without any test.
The incidents described by TedMaul and Chak sound very serious, and added to that is the problem with an unregistered vehicle in the hit-and-run that Chak witnessed. I'm sure you know the main reason why drivers think pedal cycles ought to have number plates--drivers fear being hit by someone piloting an unregistered vehicle which may be very difficult to trace, if at all. This scooter rider committing a hit-and-run offence is very close to that scenario. That's not even to mention how, not entirely unlike certain bike riders, the people in these two cases are clearly a danger to themselves as well as to others. (Always with the caveat that drivers kill and maim far more, etc.)
Met launched a mini-crackdown on them recently. It's classed as driving a motor vehicle with no insurance and it carries a £300 fine and 6 pts on your driving licence.
https://www.standard.co.uk/news/london/met-s-safety-team-target-dangerous-electric-scooter-riders-on-the-roads-and-pavements-a4118041.html
I don't mind them using the cycle lanes but at full whack they go a bit too fast and the riders never shoulder check when they move or indicate IME