There are some roles where you would get in with little experience, such as Ops Assistants although as you say some of them want some Aviation experience. Certainly where I used to work there were a couple who started as assistants with no aviation experience at all.
A route in could be to start off in another role like customer service or on the ramp. There are plenty of those jobs going at various airports. Being in Farnborough you are also near to Heathrow, plenty of jobs going there.