MMEmatty,
I did baggagehandling whilst at uni for 3 summers in LHR 95 onwards. Shouldn't be a problem as handling agents look for this sort of seasonal workers.
Airport Authorities are obviously very strict on airside passes - Get a disclosure CRC (
www.disclosure.co.uk) and get your work references sorted and anything that will cover you for the last 5 yrs ie contact name/address for a ref. at uni/school. If you go on the servisair website and email their admin dept they will give you the address for who to contact at MME but you may have more chance at busier airports.
Good luck
WTD