There are four reasons why the Thames Estuary airport won’t be built (IMHO).
1. It would necessitate closing down LCY.
2. Planes taking off to the west which is the prevailing direction would go over London anyway (negating one of the reasons for moving it from LHR).
3. For one third of the year the winds are such that the aircraft would have to come in over London as well.
4. Because the Thames Estuary is 50 miles further east than Heathrow, the aircraft would have to be brought down through Dutch airspace.
(At the moment you come down into LHR skirting the edge of French and Dutch airspace, but the Estuary airport would put aircraft right into it – and it would also affect Stansted airspace).