Welcome to the Forum @Frederick!
Awesome to hear you're a fellow Londoner and also an e scooter enthusiast.
I don't know enough about being able to register scooters to fully answer your question. However what I do know because of the mechanics involved with e scooters and the newer form of technology, most UK insurers tend to stay clear.
With that said, I would speak to scooter distributors directly such as:
Inokim (near Great Portland Street station - you can call them after a quick google)
Scootera (quick google and feel free to call him too)
These guys should have more information regarding it. Keep in mind, although some scooters are as powerful as motorcycles and mopeds they won't be 100% officially be recognised as such. There wouldn't be a state licensed test you could take yet either. But I could be wrong.
Look forward to hearing more about your investigation
Other London riders can chime in too
@ED209 @Afeez Kay