Well - the club where I fly managed to arrange a group visit to Air Traffic at Brize Norton. The guys at Brize made us extremely welcome and were more than happy to show us round and spend time explaining how they operate. This was a couple of days before Fairford, so they were fairly busy at the time.
What I found most enlightening (and as a new PPL reassuring) was their attitude to GA. They were very much of the view that they're more than willing to help us where their workload permits. They also stressed that we can help ourselves by engaging brain before hitting the PTT, speaking clearly, succinctly, and being clear about our request and intentions. Basic stuff really.
My attitude to controllers changed significantly after this visit.