An electric scooter requires tax and insurance if it is to be used on the public highway. (Additionally, the rider must wear a crash helmet and, if using the scooter at night, display lights). For the purposes of the Road Traffic Act, the law regards the definition of a 'public highway' as extending to any private land to which the public have free access. So it's still illegal to use an electric scooter on, say, a supermarket car park, even though it's actually private property.
The law, quite rightly, prohibits the use of electric scooters on public footpaths:
http://www.met.police.uk/askthemet/514.htm
Chris



