It was the Mercedes driver’s fifth win at Silverstone, which equalled the tally of Scot Jim Clark and Frenchman Alain Prost.
Mercedes’ Valtteri Bottas finished second with Ferrari’s Kimi Raikkonen third.
Vettel was third with two laps to go when he suffered a front-left tyre failure and had to settle for seventh.
‘It is never easy,’ said Hamilton. ‘The feeling I can’t describe. It is amazing to be out here and I am so proud to see all these flags everywhere.
‘The support has been immense and I am really proud that I could do this for you all. The team has been faultless. Valtteri has done an exceptional job as well, so it has been the perfect weekend for us.’
Asked if he was going to win the championship, Hamilton replied: ‘That’s the plan, but there is a long way to go.’
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