I do believe the Heathrow incident was a bit of dull thinking. IIRC, there was a heightened threat level in 2003 or 4, and the Met Police deployed mob-handed to LHR. They realised that they were still insufficient in number, so asked for military support, which was granted.
The Household Cavalry in Combermere Bks, Windsor were the obvious choice. HCav (being light recce) are equipped with Scimitar. That's what they deployed with. I would imagine the CO was asked for his support for the security situation at LHR, and saw no problem in taking his vehicles, which were well suited to guarding an airfield. Apparently no-one in the Police higher-ups or government had thought through that the Army were very likely to do a comprehensive job of what was asked of them. Equally, the blue-blooded CO of HCav would have no issue dismissing the rozzers' view of life.
Red faces all round on the part of the fawning civvies, AQ attack on LHR deterred, or was bollox G2 in the first place.