Try looking on Aviationjobsearch.com
They are advertising for Handing staff at LGW, LHR and various other airports. All positions are through either Aviation Resource or Premier Work Support which are bother recruitment agencies.
If you fit in and the airline you work for like you then they may offer you a contact with themselves directly. If it is for the short term though you can usually stay with the agency for as long as you like, and then leave when you like. From experience most training courses are only 1 week in the classroom then a few days supervision on the ramp so you will still have plently of time once your trained up.
Whilst i was a STN we all started of with an agency and were soon offered a permanent contact. Most positions like this are normally advertised through agencies but check out the website i mentioned and you should find something.
Also BA were recruiting direct a few weeks ago. Go to BA.com and check careers to see if they are still looking for staff.
Hope this helps.
Regards.