I'm from Australia, and I applied for LGW, got an interview, had to pay my own airfares and accomodation to London (which was a fair amount of money to spend for an interview with no guarantee of success! Thankfully it paid off though! Still waiting for training though
) - and I was the only person who was non-UK at my interview...
So yeah - I guess it DOES happen... As long as you hold an EU passport - there's no reason for non-UK residents to not apply (I have a Belgian passport)...