. There are zero long haul routes that BA operate that rely on connections from Europe in order to operate.
Really? Not a single long haul frequency or route would be dropped if BA stopped interlining with Finnair, JAL and Iberia across Europe and parked the A320 fleet. Is that what you said or am I misunderstanding you? Given the sheer volume of international to international connections across Oneworld LHR I suspect you may me misguided. Some Spanish BA flights are almost majority Japanese at certain times of the day.
btw BA don't want a third runway, their business model is dependent on rinsing a semi-captive market. Competition would explode if capacity was increased to the proposed levels.
Also you say "double capacity at LGW" to aid p2p when there is considerable free capacity at LTN/STN/SEN for inbound leisure. You don't NEED to build a new runway anywhere quite yet for that market, regardless of what GIP might want.