The security situation makes it very difficult these days.
When I was 16 (24 years ago) I did work-experience with Dan Air at Newcastle, and was issued an airside pass. Nowadays you have to have references and a Criminal Record Check to get one, which is a lot of trouble for a company to go through for very little benefit to them.
That said, at a bigger airport there is no reason why you couldn't gain valuable experience without having to go airside. Your school or college may be able to help when asking for work-experience attachments, or perhaps the local careers office.
Best of luck.