Jonathan,
I have visited the old LATCC at W Drayton a number of times and found it fascinating. I have yet to visit Swanwick, but am open to tempting offers!
Whether sectors are part of TC or not is really not the issue. If I am talking to an airways sector, as opposed to an approach control, the norm, if not the rule, is to use the full, five-letter callsign throughout. I am only wondering why.
Will/Timothy, whatever you want to call me