Upper Heyford / HS2
All completely mad - third runway at Heathrow, and/or reinstate Upper Heyford with Shanghai-type ultra-high speed monorail linking the lot to London, running beside the M40 which can be enhanced at certain points as well. Your £50 billion would go one hell of a lot further on infrastructure the right side of London. Indeed move HS2 a bit to the west and add a spur through Upper Heyford halfway to Birmingham having touched Heathrow. Heathrow 10 mins from central London, Upper Heyford 25 mins and Birmingham 45 mins.
If 45 million UK citizens need to go all the round or through the middle of London to get to a new Boris/Foster island in the north sea, that does come across as being a bit nuts?