As far as I know, the first class area was modified for that tour and tech crew was BA.
I don't know, but I assume they would've been BA as well; obviously hand-picked.
Would've entailed a lot of expense and training for RAF crew to be used.
Maybe someone from BA could elaborate.
For internal travel while she was here, she used an Air NZ BAE146 and RNZAF 727.
PS: Just out of interest, her first ever commercial flight some years ago was on an Air NZ B747-400 LHR-LAX-AKL with modified first class compartment.