Hi Ben,
Sounds like me a few years ago! I also had work experience to find when I was in Year 10. I wrote a heart-felt letter to the work experience co-ordinator at BA about a year in advance, and was told they hadn't opened their diary yet, but would keep my letter until they did. Result was a week at Cranebank. Most of the time I was working on producing a presentation on the basic theory of flight for new entrant cabin-crew. However, the best times were in a 747-classic sim watching an Operator Proficiency Check! After the guys had finished, the training captain set up the sim for me to take-off and land at JFK, whilst in between, he demonstrated a little-trick they used to do, namely, flying between the towers of the WTC... Needless to say 9/11 was extra-chilling for me.... Also, on one of the days, I was allowed to follow and take part in a 747 Safety Equipment & Procedures Day. Extinguishing galley-fires, jumping down slides, and role-playing on-board emergencies...! Was all good.
In the Sixth Form, I managed to get a second place with them, using my contact from the first time - the Chief Longhaul Pilot. He managed to sort out two days of Management Shadowing, though there wasn't actually much of what the name suggested! I did however get a look inside Concorde at the hangar, and a jumpseat ride LHR-MAN-LHR on a shiny new A319; much more interesting!
Obviously a lot has changed since then, but I guess the moral of the story is "Ask and you MAY receive, knock and the door MIGHT be opened to you!"
Cheers,
Shortcut
PS Forgot to mention, it was on that jumpseat ride when I was being chaperoned by a long-term off-sick SFO that I was put onto good old PPruNe!