They're illegal in the same way that if you sticking four wheels on a fridge and driving it down the street is also illegal. They're not road worthy, and you can't use them on footpaths in the same way you can't cycle on footpaths.
I'm seeing more and more on my commute, but it's the difference between a few people buying their own from Alibaba and a company installing them across the city. The former's unlikely to draw attention from the police, the latter much more so.
Basically, the laws say that your vehicle must be licensed to be used on a road unless it’s a bicycle/pedal assist bike/a few other categories, and there’s no mechanism for licensing some of the newer transport options. The laws also say that a vehicle can’t be used on the pavement at all, so there’s no way they can be used on a public road at all.
And have you ever seen a picture of most British cities - there’s barely enough room for cars and pedestrians sometimes, never mind a whole separate lane for cyclists/etc.