Most of the airlines ground handling uniforms that you will have seen will be worn by Handling agent staff. It's an Airlines way of having a dedicated team without the Tax and PAYE implications of recruiting their own staff.
Getting into an Airline does indeed seem impossible to those on the periphery of the Industry. Handling agents tend to recruit locally via newspapers and local job agencies.
You could also go online and search for the various Station Manager & HR contacts at BHX. Most airport websites list contacts for all their resident airlines.
It says on here that you're 18 and a frequent flyer so am presuming finances aren't a major issue. If that is the case (if not, i apologise for my presumption) and you really want to get into an Airline why not apply for an Internship or that you will work for them for free on the proviso that they give you a job afterwards. You have nothing to lose via this method and am sure they will applaud you for thinking outside the box.
Good luck & am keen to hear how you get on with your search.