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Verstappen's podium finish left him 57 points clear with five rounds remaining.
Hamilton, who has been racing competitively since he was six, said he has also battled with depression as an adult, and has found it difficult to open up about his journey.
Italian Antonelli, who has won one sprint and one feature race for Prema Racing in Formula Two this year, will join George Russell at Mercedes, with Hamilton switching to Ferrari.
The two have been together through Hamilton's 12 years at Mercedes and their radio exchanges have become part of the language of the sport for a global television audience.
The decision means that McLaren's Oscar Piastri finishes second with Ferrari's Charles Leclerc in third.
The 39-year-old Mercedes driver's last win before Silverstone was in Saudi Arabia on December 5, 2021, and Sunday was a record-extending 104th of his career.
Red Bull's Dutch driver has extended his championship lead to 69 points.
It was Verstappen's first DNF (did not finish) since retiring from Albert Park in the 2022 race and ended his run of race wins at nine.
The action starts in Bahrain on Saturday.
The 39-year-old Briton is set to replace Spanish driver Carlos Sainz at Ferrari.
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