Based on current schedules, it seems that a new runway will not be ready for use until 2024 or later. If we assume modest growth of London area traffic - say an average of 2% per year, then we're looking at an extra 25m or 30m passengers by 2024 - the equivalent of Luton *plus* Stansted combined.
Would it really hurt Heathrow / Gatwick financially that much if there were 2 new runways to be complete by about 2025 ?