Why not?
There are underused runways already at Sothend and Manston. If you're going that far out, those would be cheaper. Cheaper again may be putting money in to speed up the rail links to Birmingham and Southampton - bring those travel times to under an hour and they become feasible. Considering a high speed link to Birmingham and Manchester will have to be under consideration now the Channel Tunnel one is finished, diverting it through Birmingham Airport wouldn't be too much of a hassle.
There's another problem with building in the Thames Estuary and that is that we don't know what sea levels will be like in the future. In that case you have to build for a worst case scenario, which means lots and lots of money.
Ultimately, it'll go to the most economically effective solution and I can't see that being in the Thames estuary.