McLaren stars Button and Hamilton, in collaboration with British Grand Prix sponsors Santander, on Thursday unveiled a vision for the future with the London grand prix.
The 14-corner, 5.1km circuit would flash by a number of iconic landmarks around the capital, including Buckingham Palace, Big Ben and Trafalgar Square.
It has to be remembered the concept is nothing more than fantasy F1, with no official plans proposed or in the pipeline for the event.
It is merely a fanciful idea, portrayed via CGI technology at the Royal Automobile Club on Pall Mall, with Button beating Hamilton 2-1 in a best-of-three one-lap challenge.
"Having been immersed in this project, having helped to shape this track, it feels as real to me as anywhere I've raced," said Hamilton.
"Jenson and I worked in the simulator to provide some useful feedback to inform the circuit design, so this is far more than whimsical thinking out loud.
"I have to say, this is an utterly epic track and would produce the most stunning and compelling Formula One race.
"A grand prix here (in London) would be the best thing in the world, the biggest event, sensational.
"If you add an event of this complexion to London's staggering roster of world-class sporting events, it surely would have to own the title of the ultimate sporting metropolis."
Appreciating the prospects of a race around the streets of the capital, Hamilton said: "How many people in London? How many would turn up to this grand prix if you had it in the summer?
"The turnout would be phenomenal. It would be millions."
It is clear, however, there is an appetite for a London GP, which has long been one of F1 supremo Bernie Ecclestone's dreams.
Plans to turn the Olympic Stadium in Stratford, east London, into an F1 track is one of five bids on the table being mulled over by the London Legacy Development Corporation (LLDC).
However, the logistical and financial hurdles for either plan are considerable, with the belief neither are feasible.
Eight years ago F1 staged a demonstration run down Regent Street that attracted nearly 500,000 people.
However, then Mayor Ken Livingstone poured cold water on the plan of a race around the capital due to costs.
Ecclestone has apparently offered to put his hand in his pocket to ensure the event goes ahead, one he has long dreamed of.
Ecclestone said: "The idea of an F1 street-race in London is something I have had for many years. It would be magnificent.
"A couple 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 few years back over half a million people turned up to watch F1 cars parading through the streets of the capital.
"So the public's appetite for a London Grand Prix is huge, as I am sure it is with the F1 teams and sponsors."
Unlike Hamilton, Button was a little more sceptical as he said: "Personally, do I like the idea of having a London Grand Prix? Yes, the more grands prix in the UK the better.
"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, a great hypothetical track to drive."
It has been suggested by marketing experts, however, a grand prix could generate up to £100million in revenue.
Current Mayor Boris Johnson has on Thursday pondered whether there is "a really good economic case" for a race.
However, Johnson appreciates the issues likely to arise, adding: "I am always interested in projects that attract jobs and bring growth.
"But the question of air quality and noise impact will have to be looked at.
"I am broadly positive providing we can satisfy the air quality and noise issues."
Certainly bookmakers William Hill are not convinced as they offered odds of just 1-33 it does not arrive until at least 2016.
Spokesman Joe Crilly said: "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."