I have passed this regularly for some years, and also have noticed the progressive decline in usage by GA aircraft here, from what was once a substantial operation - which was when the LCY runway capacity was much more stretched than nowadays. The place seemed deserted all through the Olympics.
A good example is to look at the Google Maps overhead image of the airport, which is dated this year, 2012. The main terminal is fairly full, obviously taken at a busy operational time. Jet Centre has just one aircraft on remote parking, nothing in front of the Centre at all.
I wonder what their commercial arrangement is with the LCY owners, and whether they can be given the heave-ho in favour of someone else with a bit more commercial nouse, and benefit to the airport overall.