To ride a Moped up to 50cc:

You must be the holder of a UK driving licence which has two parts:
- Photo card
- Paper counterpart (unless you have a old style paper licence).

(If you hold an EU licence you must apply for a UK driver number).

After successfully completing a Compulsory Basic Training course (CBT), within 2 years you must pass: a motorcycle theory test 2 practical tests - modular 1 and modular 2

After this you can ride a moped without L plates, and carry a pillion, providing the bike is under 4kw.

You are not allowed on motorways.