@parabellum, probably it was because the CAA thought of doing display flights as either areal work or commercial flying. And in that case you have to advise the company about hours and times and on the other hand need a permit from the company. Anyway, i'm not flying in a UK airline, just in a small european one and employment laws are different in each country, with that the required or not required permit from your primary employer.
EU-OPS however mandates that someone keeps a master list for FDT calculation. usually that would be the primary employer, but it can be the employee or the secondary employer as well. However only commercial hours need to be take into account as far as i know. Privately flown stuff doesn't matter.