>>1630183UK (really GB, not sure about NI) rules are maximum 250W, and 15.5mph cut-off for the pedal assist (you're free to pedal as fast as you like on your own, of course. A lot of people including police don't actually understand this and think there's a hard limit of 15.5mph full stop)
Anything else is a motorcycle or "moped", and you need to get a licence, register, tax and insure it. It really is that simple. if you build your own you also need to get it inspected and signed off ("type approved"), which isn't as simple as it sounds and can cost a lot more than you'd think. And no, buying a chink hub motor and rigging it up to a BSO isn't actually allowed, despite the abundance of kits on ebay etc.
basically, just ride a normal bike. The ebikes that are actually legal barely offset the weight of their battery, and even they attract attention. it's not worth it.