Davies has to answer two different high level questions
1. Future hub capacity for the UK.
2. Future total capacity for London and South East in particular.
Given that, I would agree with Dave Reid's list but add an option of 3 at Heathrow, 2 at Gatwick and 1 at Stansted. If you believe the forecasts, the London system as a whole will be very short of total capacity even with R3.
The comments on HS2 are unbelievably negative. Currently the time to allow from Leeds or Sheffield station to Heathrow airport door by rail is around 4.5 hours--- 2.5 to London plus 1 to the airport plus 1 for things to go wrong. Via Old Oak Common that should roughly halve.
Get the Western curve from LHR towards Reading done now, get HS2 done, get the Northern Hub scheme done in Manchester and that combination will make a big difference to access from most places north of Watford to the international network.