"If you have a full car licence you may ride motorcycles up to 125 cc and 11 kW power output, with L plates (and/or D plates in Wales), on public roads, but you MUST first satisfactorily complete a CBT course if you have not already done so."
http://www.direct.gov.uk/en/TravelAndTransport /Highwaycode/DG_069867
"If you passed your driving test before 1 February 2001 you are qualified to ride a moped without L plates (and/or D plates in Wales), although it is recommended that you complete CBT before riding on the road. If you passed your driving test after this date you MUST complete CBT before riding a moped on the road."
So, you MUST pass the CBT before riding a 125. You can only ride a moped without the CBT if you passed your car test before 11th Feb 2001.
"A full car licence does NOT exempt you from the Theory Test anymore."
http://www.motorcycle.co.uk/getdoc/b464be52-72 b4-4044-9be9-664b1006c00a/Licence-categories.a spx