Firstly the NATS advice concludes that any new runway, will have an impact on the others within 50nm (see conclusion page 44)
Not necessarily.
NATS' analysis, in that document, is that a third runway at Heathrow would have no impact on capacity at Gatwick (22nm away). Equally, Gatwick R2 would not affect Heathrow's capacity. See pages 41-42.