"Lewis feels that he is in such a tough championship fight that he needed the days off after Austria," Mercedes team boss Toto Wolff explained to the crowd at the F1 Live event in Trafalgar Square.
"But you can see him in Silverstone."
Hamilton had announced on social media that he was taking a two-day break, posting a picture of him and friends on the steps of his private jet. He is due to face the media at Silverstone on Thursday.
Mention of the country's most successful racing driver, a man with 56 wins to his name and huge support who will be favourite for a fourth successive British Grand Prix victory on Sunday, drew some boos.
Hamilton was the only absentee of the 20 drivers who performed tyre-smoking spins, or "donuts", in their cars on individual runs along Whitehall to the crowded square and back.
Ferrari's championship leader Sebastian Vettel, 20 points clear of the Briton after last weekend's Austrian Grand Prix, had plenty of fans in the crowd and was not shy in his title rival's absence.
"I don't know why he's not here," smiled the German, who drove into Hamilton in a "road rage" incident in Azerbaijan last month, when it was suggested to him that maybe Hamilton did not fancy sharing the stage with him.
"We left some marks...it's great fun to go so close to the people. You can see the cheering, waving. It's been really fun. I'd love to do more laps but we'll wait for the weekend."
Jenson Button, Britain's 2009 world champion, drove fashion model Naomi Campbell in a two-seater while Belgian Stoffel Vandoorne gave the fans a glimpse of the late Ayrton Senna's 1991 McLaren.
Jackie Stewart, Britain's only other three-times world champion, was also among the guests while Mercedes' retired 2016 world champion Nico Rosberg flew in from Switzerland.
The event, organised by the sport's new owners Liberty Media, was the first time Formula One cars had driven in London since 2004.
"The sport's all about the fans," said Formula One's extravagantly moustachioed chairman Chase Carey on an evening of cars and music as well as events to showcase the sport's educational activities.
"We want to connect with the fans in every way possible and today is a step in that direction."
(Reporting by Alan Baldwin, editing by Ed Osmond)
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