There's nothing you can do riding an E- bike that can affect your driving license. Unless it's in your pocket and you ride into a canal.
this is true on a pushbike - for excessive speed the charge is "wanton and furious driving" which dates back before the motor age, but I think the cops/CPS can only use this charge when a collision has occured.
There are also charges of careless and dangerous cycling.
I'd agree that with factory built e-bikes designed for the UK or EU the only charges applicable would be the same as pedal cycles.
however with a a modified/home built bike over a certain power I think there is a very slim chance that someone could be busted for riding an illegal "moped" and that would earn points on a license but I reckon they would have to be being a complete fool on the roads (such as riding at excessive speed in an anti-social manner in a busy area) to get nicked.
I have an interest in criminology and thus check the details of every crime and road collision I see in the papers, I have been doing this for many years and other than some unfortunate collisions of riders on push bikes with pedestrians in city areas, the only other dangerous cycling case I am aware of was a lad in Reading who in 1994 took 4 ecstasy tablets as well as a fair bit of booze and then proceeded to ride fast but eratically through the pedestrianised area (causing people to take evasive action) as well weaving in front of moving buses, just months after they had just installed CCTV in town. I think he got fined about £400.
Maybe you could call it an "e-bike" but not the sort we are used to
(It wasn't me BTW)