Hybrid electric bikes, how do they work?
The class of bike you're looking at is called an Electrically Assisted Pedal Cycle, a brief summary of the law regulating these is available here. In the UK (and Europe):


maximum power is 250w
maximum assisted speed is 25 km/h (15.6 mph)


You don't need insurance, a driving license, Vehicle Excise Duty or a helmet to ride an Electrically Assisted Pedal Cycle.

It's possible to get electric bikes with more power and / or a higher speed limit. These would be classified as a moped and would need insurance, driving license, etc. You also couldn't ride them in cycle lanes and cycle paths.

Some Electrically Assisted Pedal Cycles come with an "off-road" mode which removes the speed limit. The linked article describes the legality of these as "at best, questionable".