HQ 1GP MAOTs used to do a lot of VIP work, and basically, whites or not was dictated by the type/fit/colour of the ac.
I did one job with the then PM, in a Puma, so it was greens.
Another was Duchess of York in a Queen's Flight Wessex. Definitely whites.
Another was the AOC on some jolly or other in a white Gazelle, again, whites.
Weirdest one was a civvy suit on Chelsea Bks parade square. Was a Puma again, and civil servants. Maybe someone was taking the pi$$.
No idea what goes on now, but that's as it was 10 yrs ago. I suppose you could say today, if it's 32 Sqn with a VIP then whites, otherwise greens.