Most of the time if you have a car license it also includes mopeds but ymmv.
I wouldn't go for an electric folding bike, especially on the cheap side they do suck and will only last you a few years.
If you only want to commute on it go for something like this instead of a racing/mountain bike:
Way more comfortable and excellent for commuting, but since you're from the UK you'll probably already know that. Biking is still the fastest way to get around in cities like London.