Just a thought but say Heathrow had that extra runway open today. So which airport would be affected the most by the extra Heathrow capacity? I am thinking probably Gatwick is it gets the Heathrow over spill and that LTN and STN would be mainly unaffected.
Not exactly, if you meant in ATC terms.
Majority of LHR inbound and outbound traffic is routed straight in from the west (over Wales and along M4 corridor), this is away from LGW inbounds which usually route inbound over south coast.
The holds to the north west and north east of LHR are usually the busiest at any time of year, these are both close to LTN and STN respectively.
Have a look at flightradar perhaps to get a better idea.
Gatwick expansion would probably have more impact on LCY and neighbouring airports such as Bournemouth and Southampton than directly to LHR.