well there's the whole problem in the first place, the hub model suits a few major airlines and major airports, but it doesn't make a lot of sense itself. they say they need more capacity for international business flights, but use up slots on tourist charters. they argue they need to respond to demand for flights to China, but at the same time these flights need in bound passengers from other places to fill the plane. Theres no reason for Gatwick not to expand into a "hub" of its own if they want, but Heathrow and BA dont want that.
Hubs suit every major airline its how they transport people from A to B to C .... like it or not (and I'm no fan of air travel) it's a necessary pert of business. If you look at destinations served by Heathrow trying to replicate at Gatwick would be a nightmare and would only serve as some sort of overflow so would be uneconomic for airlines (they get economy of scale at Heathrow). Heathrow does need more outbound capacity and its inbound routes serve that and can also be expanded. Gatwick really has neither (not much demand for flights in from Tenerife and Malaga to transfer on to Shanghai)
There are no tourist charters operating from Heathrow
I'm not for or against either, in fact there may be an argument for expanding both. But for me, the key point is that Heathrow is hub and business whilst Gatwick is point to point and leisure and trying to change that either won't work or the cost of doing so will be eye wateringly prohibitive