In a race with two late safety vehicle periods, reigning champion Hamilton went from pole position to the rear of the field before finishing second for Mercedes in a superb fightback.
The four-time champion seized the lead at the start and fought back after losing the initiative during two safety auto periods to register his second win at Silverstone and the 51st of his career.
Hamilton rushed back into the mix for a podium spot with the majority of runners picking a one-stop strategy until Marcus Ericsson lost control of his Sauber at Turn 1, and his fierce shunt into the tyre barrier brought out a lap 33 safety vehicle.
On what pleased him the most about Silverstone, the German said: "The history behind it, the track being really fast, and the fans".
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The Englishman clearly blamed Raikkonen, who was handed a 10-seconds penalty, for the crash and found it hard to face the Finn or accept an apology.
Bottas was fourth with Red Bull's Daniel Ricciardo fifth and Nico Hulkenberg sixth for Renault.
But the headlines belong to Vettel, who suffered a neck injury during practice on Saturday and was forced to wear supportive tape during the race, but came through for his fourth win of the season. Hamilton stayed close in third, hoping for a chance.
Lap 12 - Hamilton is already sixth, as Ferrari's Vettel keeps hold of his lead so far. Fernando Alonso was eighth for McLaren ahead of Kevin Magnussen in the Haas while Pierre Gasly finished 10th but was demoted after a five-second penalty that lifted Force India's Sergio Perez into the points. Both Ferrari and Red Bull drivers took advantage of the safety vehicle to stop for fresh tyres, but Mercedes left both of their cars out.
Hamilton kept Vettel in his sights but couldn't get within striking distance to try and snatch the win, while Raikkonen was just a second adrift at the line as the top three in the championship filled the podium. Esteban Ocon (FRA/Force India) 29.930, 8. Lance Stroll (CAN/Williams) 38.106, 14.