I also see a third runway at LHR as by far the best and realistically only option. LGW is not the right place for a new runway neither is STN or LTN. The Thames Estuary is a stupendously more expensive idea, would take absolutely years to build and somewhat unnecessary to need take the issue anywhere near that far.
Indeed the Thames Estuary could have high speed rail into London in 20 minutes, but what about those originating in the UK or not travelling to/from London? I live in the Midlands, LHR is less than 2 hours away on a good day, the Thames Estuary would be 3 hours or more! It's not the right place for an airport. Why not build a high speed underground link from LHR to London which takes less than 10 minutes?
As for LGW, what does that achieve? A split hub operation? I don't think so! FR might move to LGW, W6 might move to LGW, EZY, ZB, TCX etc. might consolidate at LGW. My point is that it would seriously endanger LTN and STN. It would destroy the London "Airport system" whilst expanding LHR would maintain it. Why?
Because LHR adds both hub and indeed point-to-point capacity in it's own right. More to the point it allows airlines from the other airports (mainly LGW) to move into LHR if that is where they want to be. The result is that it would free up slots for airlines who do actually want to fly from LGW (or STN, or LTN etc.) and are not just there because they can't fit into LHR. Effectively you've increased capacity in a more cost efficient way and helping not just LHR but all the other London airports to thrive and build stronger relations with their airline partners.
A second LGW runway would clearly not solve the problem of constrained slot capacity at LHR so you'd still have capacity taken by airlines at LGW who actually want LHR. The extra capacity a second runway would give LGW could quite easily be largely taken by airlines relocating from the north London airports and would only leave STN and LTN to cater for a lot of the "new" capacity (if they were to even survive at all). The end result is spending millions of pounds and you still haven't solved the problem you set out to achieve. It risks actually restricting growth in the longer term future just as much as doing nothing at all.
The same pretty much goes for the Thames Estuary airport unless LHR was to close down and all the business involved with it in West London would have to move! Absolutely crazy!