Actually a third runway at heathrow to start with and reduction of APD in the regions would be a good start.
However, on the subject of lack of capacity at LHR, is there a lack of capacity or could the capacity be better distrubted, for example I believe I asked this question before without answer, do BA/AA need to operate the number of flights daily that they do between LHR/NYC. If they are all operating with a high LF then fine, but if they are not surely they can consolidate and or introduce larger aircraft such as the soon to arrive A380 and release slots for say Chinese services.