Integral to the consultation process, Button and Hamilton took to the streets of the capital in CGI simulators to show what a race around some of the world's most-famous landmarks could look like.
But as Sky Sports commentator David Croft mentioned at the start of the event at the Royal Automobile Club on Pall Mall, what was being portrayed was "fantasy".
That did not stop Button and Hamilton having some fun, initially in the design process alongside British Grand Prix sponsors Santander, and again on stage as they went head to head.
Taking in several iconic landmarks around the 14-corner, 5.1km circuit, including Buckingham Palace, Trafalgar Square and Big Ben, Button beat Hamilton 2-1 in a best-of-three one-lap battle.
Both drivers can certainly envisage the possibility of two races being staged in England at some stage in the future, with London joining the British Grand Prix at Silverstone.
Button said: "The layout looks great, but of course there is a lot more to it than just having a good layout.
"It's been done in other cities, like Singapore, and of course Monaco is a little bit special as it's been there for 70 years.
"I don't know how difficult it would be to get a London grand prix up and running, but all we know is that it sounds like a great idea.
"Silverstone is very special, but it would be nice to have another grand prix on our doorstep.
"Obviously, the London track is a great hypothetical one to drive, but it is as appealing as the reality of the Silverstone circuit."
Hamilton, who has beaten Button 5-3 in races this year and out- qualified his fellow Briton 8-0, took the London GP setback with good grace.
At least the 27-year-old was able to agree with Button when it came to the experience of driving around London, even if it was in simulators.
Hamilton said: "Having been immersed in this project, having helped to shape this track, it feels as real to me as anywhere I've raced.
"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."