I rarely fly GLA anymore, having moved from working up that way to down in London.

Oh dear, sorry you had to slum it with normal security but glad you got through quickly. A standard CS replay can be annoying I agree, but not sure I would have contacted BA to complain myself, although the agent seams to have completely missed the point in this case which no doubt has caused additional frustration, essentially what are you wanting BA to do?

If I were still working in customer service, I would issue a sincere apology and then pass the complaint on to the airport for investigation/action; not exactly sure what else BA could do than highlight the issue to the airport and request all staff are reminded that Business UK should be allowed to use Fast Track.

In hindsight, perhaps asking to speak to a manager in the airport could have addressed the issue and the training need there and then.