EDI will have a few handling agents. I'm almost certain the only self handling airline left there is BD
? (Correct my if I'm wrong)
Aviance definitely have a presence handling BA
and others. Servisair are also up there. A simple ring to the airport information desk should be able to give you a list.
As Pe@rson said, an offer to work for nothing could be good for both you and them, but don't expect to be doing anything too exciting. Getting an airside pass is becoming more and more of an issue so I wouldn't expect to be wondering through security any time soon (especially if you're under 18!) so the best you could hope for is check-in (if they're willing to train you etc). Having said that getting airside may be worth a shot; get a CRB/Disclosure Scotland check carried out and they might give it consideration.
How about casual summer work? Most of the handling agents will be employing for the summer, although perhaps not to the extent of previous years. You'd get your experience and you'd get paid... a little!
Small regional airports will probably be more helpful. Or how about a local flying club?
[Edited 2009-01-12 16:16:38]
Gale force fog... don't you love it?