To use a motor vehicle legally on the road, it must meet certain legislation and construction requirements. These also apply for e-scooters, meaning they would need to be registered, insured, taxed and comply with all the relevant safety standards.
Unless a privately owned e-scooter, and its rider, could meet all the required legislation, using one on the road is illegal.
Separate rules apply for those used in designated official e-scooter trial areas, where rental e-scooters may be used on the highway.
Use an e-scooter on the pavement in modern times and you run the risk of a fixed penalty notice.