The defending five-time world champion clocking fastest lap on his final lap to finish 25 seconds clear of Mercedes team-mate and nearest title rival Valtteri Bottas after an action-packed contest.
The Briton moved 39 points clear of the Finn behind in the title race, but Bottas was unlucky with the timing of the safety car which effectively gave Hamilton a free pit stop.
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Pierre Gasly finished fourth ahead of his Red Bull team-mate Max Verstappen, whose race was compromised by a late collision when Sebastian Vettel of Ferrari drove into him, and Carlos Sainz of McLaren.
It was Hamilton's seventh win in 10 races this year and the 80th win of his career. He had shared the British Grand Prix record of wins, on five, with fellow-Briton Jim Clark and Frenchman Alain Prost.
Daniel Ricciardo was seventh for Renault ahead of Kimi Raikkonen of Alfa Romeo, Daniil Kvyat and his Toro Rosso team-mate Alex Albon.
"What a day," said Hamilton. "To all the crowd, thank-you so much for coming out." Hamilton, who stopped on his slow-down lap to collect a British 'Union Jack' flag, added: "I love you Silverstone. I appreciate everything and the opportunity to be a part of this.
"I couldn't have done this without these guys or without my team." A glum Bottas said: "Congrats to Lewis... It wasn't my day." A much happier Leclerc said "It's probably the race I've enjoyed the most in my career." The safety car was deployed when Antonio Giovinazzi spun into a gravel trap in his Alfa Romeo - gifting Hamilton a 'free' first, and only, pit stop.
The luckless Bottas, on a two stop strategy, had already pitted before the incident.
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