If your e-bike doesn’t meet the current regulations – either because the motor is more powerful than 250W, or if it assists you when you’re riding more than 15.5 mph – it will need to be registered, insured and taxed as a motor vehicle. In this case, you will also need a driving licence, and you must wear a motorcycle helmet.
These other kind of bikes (also called speed pedelecs) cannot be ridden on cycle paths and must be approved by the DVLA. So while it’s easy to de-restrict an ebike to get the motor assisting you with higher speeds, it is not very wise to do so, both for regulatory and safety reasons.