Last time I was there I watched direct flight to Chile leave with LAN ... Do not know if LAN are still on this route
LAN have two daily flights to Europe these days, one from SCL flown with a B788 and one from LIM flown with a B763, and both flights have MAD as their destination. The SCL flight has a short stop at MAD and continues to FRA. I have flown with LAN on FRA-MAD-SCL a number of times, even when they flew it with B763. Nowadays I prefer a more direct routing and fly with Air France OSL-CDG-SCL (next flight will be on 11 March).
Flying through LHR has never been an option for me on my long haul business flights, but for visits to our subsidiary in Hampshire LHR is perfect.
But let's return closer to the topic - the capacity of London's airports. In 2013 London's five airports LHR, LGW, STN, LTN and LCY had close to 139 million passengers and with only 6 runways available that gives an average of more than 23 million passengers per runway. In Mancunian terms that is 1 million more passengers than you had in 2014 without being allowed to use the second runway. Since I mentioned CDG above, this airport has four runways and with 62 million passengers in 2013 that gives only 15.5 million passengers per runway. AMS, another competitor to LHR, has an average of just above 13 million passengers per runway (only 4 of its 6 runways can be operated on the same time). The only conclusion I can see for London and its airports from a safety perspective is to give three airports carte blanche to build as many runways as they need/want to invest in, and the three airports for me are clearly LHR, LGW and STN.