840,
What such fast rail links will make feasible, is wiping out much of the (pointless) domestic air travel into various London airports - hence freeing up capacity at pretty well all of them. If all point-to-point domestic travel were by ground, I suggest you'd have loads of empty seats. Aggregate two or three A319s into a single 321 (or 767) from each of the main domestic airports timed to meet the main wave of evening intercontinental departures (for connecting traffic) and you've suddenly saved yourself a load of slot pairs.
Or, take the Dutch and Swiss model and have good, regular high-speed trains out of the airport railway station to each of, say, Manchester, Birmingham, etc. and likewise you're freeing up capacity. No-one flies long-haul into Amsterdam and then changes planes for Rotterdam; you go downstairs and get on a train.
BA could even consider code-sharing onto rail services (and this should be made easier as European rail operators move beyond Stephenson's Rocket and co-ordinate things a bit). Imagine being able to check-in for your flight to say, Sydney or LA at Gare du Nord, or Midi, or Centraal, 2 hours or so later be at Heathrow and just clear security and onto your flight. Easy. Probably time saved over having to schlep out to Roissy, Zaventem or Schiphol, do security, wait, taxi out to the Polderbaan (ie. drive half-way to London), stack over Biggin, land, taxi, go to the FCC, etc.