My understanding is that, provided you are riding a 'legal' ebike, then it is a bicycle and not classed as a mechanically propelled vehicle. There is the offence of drunk in charge of a bicycle, but I don't believe the road traffic act applies. Of course, if you are riding like an idiot then I'm sure the boys in blue will come up with some law to prevent you doing so. As with so many things in life, just ride sensibly.
I have had the pleasure of being pulled over, (perhaps too strong a term) on two occasions around 11.45pm after having consumed a couple of 'sharpeners' at the local pub. The first time, the officer enquired if the bike was electric, as he could see the red lights on the handlebars as he cruised past. Clearly he was intrigued and when offered a go he took it up the road for 200 yards and back, much to the amusement of his colleague. We had a little chat about ebikes and off he went.
On the second occasion, the officer said," no problem sir, I just wanted to commend you for making sure you are visible and safe, we could see you from a mile away". I was wearing hi-viz and have two powerful rear lights. On departing he enquired, "have you had a drink this evening sir". I said that I had enjoyed a couple and was on my way home. "Ride safely sir". And that was it, not a hint of animosity, and I was a little worse for wear! Nothing in life is for sure, but if you are sensible, I don't think you will have a problem. It is pertinent that my journey home from the pub is rural and very dark and quiet, and a grey haired old fart dressed to the 9's in hi-viz at that time of night is bound to arouse some curiosity from passer's by as to what on earth I am doing there!!