There's some people at USAF and USSS losing their minds over the issue as we speak.
That just means they hit everything. Also, BA was government owned for a while, which is a little different from the POTUS flying in on a Southwest plane.
British Airways, as it then was, was privatised in 1987.
Back in those days there was the Queen's Flight in the RAF dedicated to transporting members of the Royal Family on shorter trips, latterly using BAe146 aircraft and Wessex helicopters. On longer trips they used a VIP configured VC10 from 10 squadron.
As part of the efforts to modernise the perception of the Royal Family and cut costs for the British taxpayer, things changed from the mid-1990s.
The Queen's Flight was rolled into 32 squadron which was an RAF Communications and VIP transport Squadron. The Royal Family generally travel overseas on commercial flights or charter commercial aircraft.
The RAF operates / has access to a small number of VIP aircraft for the use by Govt ministers and the Royal Family for official business. So
The King's Helicopter Flight - 2 x AW139. For use by the King and senior working
32 (The Royal) squadron - 2 x Envoy IV CC1 (Dassault Falcon 900LX). RAF owned. Civilian registered. Flown by mix of military & civilian pilots.
10 squadron - VIP configured A330 MRTT, part of the RAF fleet operated under the PFI deal.
A321LR on lease and operated by Titan Airways on behalf of the Govt.