I would certainly go for them - the paying public have a right to expect people taking them up for money are properly licenced, etc etc - I would certainly expect it of any airline, as mentioned above.
However, be aware that the CAA would untilmately be powerless as most of the legislation is possibly invalid anyway - certainly there is no provision in the Civil Aviation Act to allocate money for the investigation of "crimes" by the CAA. Probably getting the Air Transport Licensing boys in would be more effective.
Phil