Following reports on Thursday that F1 chief Bernie Ecclestone is trying to get the idea off the ground, a computer-generated vision of what the race might look like was released.
81-year-old billionaire Ecclestone has long backed a street race in the capital although money, political and environmental concerns have all proved insuperable obstacles in the past.
"It would be magnificent," said Ecclestone, adding that the race has nearly happened in the past. "A couple of years ago we came very close to an agreement with the City of Westminster and the Mayor's office but we ran into the small problem of cost."
A model of the track, designed by leading architects Populous, made light of an obvious problem as it threaded through the monumental Admiralty Arch off Trafalgar Square.
That would be very much an accident waiting to happen, given that ordinary traffic goes through its three narrow arches in single file on the way to the Mall and Buckingham Palace. There is no way around it.
McLaren's Button, the 2009 champion, said he loved the idea of racing around monuments and landmarks in principle anyway.
"Do I like the idea of having a London Grand Prix? Yes, the more grands prix in the UK the better," he said. "But I'm not sure where it would be. There was talk of using the Olympic Stadium which could be quite a lot of fun.
"I'm not sure you would be able to close down London for a grand prix but it's a nice idea though," added the 32-year-old who has yet to stand on the podium of his home grand prix.
Bookmakers William Hill were sceptical. They offered odds of 1/33 that there would be no race in London until at least 2016.
"The idea of a London Grand Prix is a great one in theory but in practice it will take a great deal of preparation and we cannot see it happening for some time," said a spokesman.
Ecclestone's previous discussions were with the city's former left-wing mayor Ken Livingstone but it came to nothing.
The current rightist incumbent Boris Johnson, a famously keen cycling fan who has also penned the occasional car review in his journalistic career, expressed qualified support.
"I am always interested in projects that attract jobs and bring growth," he said while expressing concern about air quality and noise.
As other critics observed, London is not a city in need of more congestion and road closures with public transport already creaking and crowded.
The possibility of using the area around the new Olympic stadium in east London has been mooted, with one of the companies on a shortlist to take over the facility after the Games talking of putting on a grand prix there.
Ecclestone denied involvement in that bid when asked by Reuters but has said he would be interested in any proposal once the relevant permits were obtained.
Hamilton, McLaren's 2008 champion and a winner at Silverstone, was also keen on the idea.
"I was looking over the city and a grand prix here would be the best thing in the world, the biggest event," he said. "It would be sensational.
"They never approach drivers to have any input into the design of circuits but I would be very open to help in any way if they are planning to do it, to give advice on curves and corners and parts we should be going through."