the law is quite complex on the fine definition of what is an electrically assisted bicycle and what is an electric motorcycle, its all down to design speeds and weights. as has been said, 18kph iirc for the current law, and there are some distinctions betweeen electrical assistance, in that you need to keep pedaling and the motor assists, or electrically powered, where you just twist the grip and its away. my daughter has a powabyke which can be switched between the two settings and can do an electric power only speed of nearly 15mph, with electrically assisted speed as quick as you can pedal it. the law was changed last year to complicate stuff a bit, and you can still buy electric assisted mountain bikes on ebay with a top speed getting on for 30mph, technically its a moped and should have tax insurance mot, reg doc, etc, but how does plod at the roadside prove that?
as for electric bikes, id have one if i needed to commute on a bike every day, simply so i can then save my normal bike for the weekends and holidays, saving wear and tear as well as running costs. and as ive got 4kw of solar power at home, i can charge it with green power too.