Hi,
I am more or less in the same situation as you (less the degree). I have kept a close eye on their website, various other websites they list jobs on, along with contacting them on a fairly regular regular basis and for over two years now I have had no luck at even getting a chance to apply for a ramp job. I had one interview there for a customer service agent, and from what I gather you have to be extremely experienced, as well as lucky, to get in there. From what they were saying, once you're in you stay in, with people rarely leaving, hence the lack of jobs available there. I even found it difficult to get in to Heathrow doing ramp without previous experience, and have just managed to get a job at Servisair (now Aviator) down at Gatwick. Although not completely ideal, it will enable me to build some experience so if any offers do come up closer to me (Heathrow, Farnborough) I will have something to prove I am up to it. So I would suggest following a similar route if, like myself, that is ideally where you would like to end up?