What are the rules governing these devices?
As it's a motor vehicle, the usual road traffic laws will apply.
DPP v King [2008] EWHC 447 (Admin)
"K was stopped by police whilst riding a 'City Mantis' electric scooter on a public road. The scooter looked like a bicycle except that it did not have any pedals or other means of manual propulsion and it was capable of speeds up to 10 miles per hour. K was charged with driving a motor vehicle whilst disqualified and with no insurance.
At trial the issue arose regarding whether the scooter was a motor vehicle. K was acquitted and the case was passed to the High Court following the decision of the trial judge for definitive determination of whether a 'City Mantis' electric scooter was a motor vehicle as defined in the 1988 Act. The Appeal was allowed and the case was remitted with a direction to convict. The scooter was a motor vehicle according to section 185 of the 1988 Act."
That was contained in the link already provided by
@Milkfloat but I've pasted it here separately in case you didn't read it.