These are UK subjects in UK uniform in a UK airport. I spent the early morning of Jan 1 2005 at Shannon Airport waiting for the early LHR in the duty free surrounded by not Irish service people but United States service personnel in desert fatigues buying celtic tat. Despite numerous complaints from locals the last I heard this was still the case, and that the manner in which the NCOs round them up to be boarded/get meals etc. is less than low key.
My personal opinion (as a civilian) is that military personnel have uniforms for a reason, and they are not dirt to be swept under a rug, to be transported around in closed vehicles like prisoners - if anything they should proceed through whatever passes for a VIP channel at a given airport as the local MP, alderman or dogcatcher probably does.
May I suggest that the next time a civ serv complains about military personnel wearing their prescribed clothing as in the example of the Baghdad embassy that a harassment complaint be raised? God knows they'd do it to the mil given have a chance - use their own weapons against them. Once you've sorted out government, then perhaps the private sector can be next.