Because they are military?
But seriously, I think you will find that because the RAF split the Zone task from the LARS task (and indeed the approach task) they have greater capacity for handling transit traffic. In my book that is an advantage.
PS. Not discrediting any civil unit where a single radar controller is trying his/her best to juggle IFR arrivals/deps, CTR transits and anything else that happens to want a LARS on a sunny day.
PPS. Having read the UK AIP entry it is pretty clear to me who you should call for a Zone transit.
1 General Information
1.1 Brize Norton Control Zone
1.1.1 Pilots wishing to enter the Control Zone must observe the normal procedure for joining Controlled Airspace and should make their request for
entry when 15 nm or 5 minutes flying time (whichever is earlier) from the Control Zone Boundary. Pilots should make their request for Control Zone entry to BRIZE ZONE.
ENR 2-1-21