Perhaps APD could be used to help support routes ot of the regions, LHR is 99.9% full so doing what they have done in here in NI to support long haul flights might help, much of the traffic from the regions on long haul routes is low yield VFR and lowering the economy ticket APD to say a flat £12 for all flights would encourage traffic from the regions.
I guess the problem would be where to draw the line, perhaps saying inside the M25, might work? But there would probably be a legal challenge? Or go one step further and make it £12 from anywhere in the UK, but then add a London emissions surcharge for flights within the M25 to recover lost revenue. It does seem vey odd at a time when the country needs economic growth to tax air traffic so heavily, it's akin to sealing up a business letter box and going ex directory!