Sounds like great fun as long as you get good weather, could be a bit miserable otherwise.
If you check out the laws relating to electric personal transportation Alloneword you'll find that they all very specifically refer to either 2, 3 or 4 wheeled vehicles so as it stands unicycles haven't been ruled on yet and so are temporarily outside the relevant laws.
They don't have the required equipment for road travel but we try to keep to the pavements and ycle paths whenever they're available.
I've stopped and spoken to several police officers who were all more interested in where they could get one than whether it was legal.
There's a few London er using them now as they are easy to take on the underground or buses.
WheelGo are the London outlet run by Jason McNeil. He has loads of info on his Web site.