The start of this thread uses language that I think has some misnomers.
“We” are not pouring any money into a third runway at Heathrow. BAA is. This isn’t like rail, where taxpayers pick up much of the tab, Heathrow is not subsidised.
If an entrepreneur wants to build a brand new airport, charge landing fees to pay for it, and attract airlines from Heathrow (which could only be done if it is permanently capacity constrained), good luck to it. However, it also should pay for rail and road links.
The British taxpayer is hardly in a position to fund this sort of thing, which of course would be a massive transfer of wealth to property owners in West London (given Heathrow has been there for some decades, and aircraft have become more frequent but less noisy it would seem rather unfair).
“Boris Island” sounds like a great idea, but that’s all it is. The private sector wont pay for it, the debt ladened government hardly should, so that leaves it a great idea and nothing else. Of course had previous governments not spent small fortunes on grandstanding like the Olympics or running near perpetual budget deficits since 1945 then it might be a bit different.