Ok, I've given up on looking for this sort of work experience, the deadline is in a weeks time and I've been offered a placement by my (rich) uncle's workplace in the city. It's the best option I've got, but I will give you all the information I know so that you guys don't suffer the same fate as me.
Flybe: Offer Work Experience, I sent a letter to personell, took over a week to reply, but they were fully booked on the week conserned.
MyTravel: Sent an E-Mail to them, took about a week to reply, sent another week confirming dates and info only to find out they were fully booked aswell. (That was a harsh blow).
London City Airport: Offered me a place if I was 16 or over. Unfotunately I'm 15 and still will be during my Work Experience week.
East Midlands Airport: Offer Work Experience but were fully booked.
I also e-mailed around 30 other airlines and airports, with almost all of them not replying (It angers me to think they don't care). BAA said on their website that they offered Work EXperience, but did not reply to my e-mail, EasyJet's enquiry form didn't work, so you get the picture. My advice is to contact as many airports and airlines as possible (including the ones mentioned above) and don't be downheartened if you don't get many replies. Also remember to contact them at least 6 moths in advance.
Hope this helps,
Dan.