While it is good, and not unknown to get Airside work experience, it is unusual, for the reasons given above. Quite simply, employers dont want to have workers spending all day escorting a kid around, when they could be doing more important work. Additionally, there is an insurance issue there, and possibly a Health and Safety one too. If i was you I would look for something else.
Might i recommend looking at other, airside, companies related to aviation? Perhaps companies that makes parts for aircraft, or overhaul things? Or perhaps a Training/Simulator company? or perhaps operations somewhere? I think BA ops may be Landside at Heathrow.
Failing that, why not try your local flying club? They will be very grateful for a young, willing victim, sorry, Volunteer to help wash, move and tidy aeroplanes, in exchange for the odd (free) flight, etc.