LONDON — The idea has been kicking around for nearly 70 years, and now it is Prime Minister David Cameron’s turn to confront it: whether to support the building of a new hub airport on the Thames estuary east of London or to shelve it again, even as projections for future air traffic show London’s existing airports seizing up under the strains within 20 years.

The proposed airport comes in at least two versions. The most ambitious is advocated by Norman Foster, one of Britain’s most celebrated architects, who has called for an integrated air and high-speed rail hub built partly on reclaimed land adjacent to the Isle of Grain, on the south side of the Thames estuary about 40 miles from central London.

Costs of the project, with new road and rail connections and a new barrier across the Thames that could double as a protection against surging tides and as a new five-mile-long rail link to the estuary’s northern shore, range from $80 billion to $100 billion. It would be the costliest project of its kind in Britain’s history, and might take until the middle of the century to plan and complete.

With that kind of time frame, and those costs, Mr. Cameron would ordinarily expect generous leeway in making a decision. But a tangle of factors, including unrest with Mr. Cameron’s leadership among the Conservative Party’s parliamentary backbenchers, have pushed the issue into the headlines again as a new political season approaches. Suddenly, London’s airports have become a touchstone political issue.