i thought you needed L plates for 50cc and moped ??
I was speaking to someone at DVLA yesterday (need to update my picture, be aware your licence can be void if you don't do this...) If you passed your full car test
before Feb 2001 you can ride a moped without taking a CBT, not display L plates and carry a pillion.
If you want to ride 50cc or above (up to 125cc) then you need to take your CBT and display L plates, you cannot carry a passenger, or go onto motorways, Mopeds are not allowed on motorways.