Yes the runway is long enough, there has been biz jets up to the the Gulfstream V go in and out. Some years ago there was a Dash-8 from Flybe called in on a recruitment drive, although there were no pax on board and probably a light fuel load.
Training aircraft always do get in the way! And calling it “London Oxford” shows where their future ambitions lie.
The VFR flying left years ago, then the sim centre, now the groundschool. I would think what’s left is just a matter of time.