If you passed your car test before 01.02.01 (which you obviously did) you automatically gained full moped entitlement (Category 'P' on your license; a moped is less than 50cc, not able to exceed 30 mph). Therefore, you can ride a moped, no 'L' plates, carry a pilion (though unlikely on a 'ped!) until your 70th birthday (when your license expires). You do not need a CBT; as said, you have full moped license.
However. Anything bigger, i.e, 125 cc, is a motorcycle (Category 'A'). Whilst you have provisional cat 'A' on your license, it must be validated by a CBT, which lasts for 2 years. Then, & every 2 years, to ride a motorcycle you must re-do the CBT.
Obviously, when you pass your Direct Access, you will gain full cat 'A' & be able to ride any size bike. Give yourself enough time on the course & good luck!