Heath Row,
In answer to your questions:-
1) Do the CAA regulate this service ?
Yes. All Flight Informations Service Officers (FISOs) are licensed by the CAA and are subject to competency checks every two years. Additionally the Air Navigation Service Provider is subject to an annual audit by the CAA.
2) Should I bother to complain to the airfield and or the CAA?
In the first instance I would suggest that a face-to-face discussion (not over the radio) with the FISO may resolve the situation. If not then a complaint to the airfield would be appropriate. If neither of these work then it would be appropriate to raise a Mandatory Occurrence Report (MOR) which is sent to the CAA. The text book answer would be that you should raise an MOR but the first two steps may be more pragmatic and produce better results.
It is worth remembering that the recollection of the two parties involved, yourself and the FISO, may be different. In the past I was involved in the management of an Air Traffic Control Unit, where there is a mandatory requirement that all radio transmissions are recorded; unlike a FISO unit where recording is only recommended. On one occasion I received a complaint from a pilot about an Air Traffic Control Officer (ATCO) and also a complaint from the ATCO about the pilot. Both reports were clear, lucid, unambiguous but varied in vital details. A replay of the recordings showed that both reports were mainly correct but that each report had vital errors and omissions which showed that neither party was either entirely guilty or entirely blame free.