Meanwhile, Australian driver Daniel Ricciardo finished the race in fifth on Sunday to hold onto his fourth overall position in the championship.
Lewis Hamilton was set to win his sixth home grand prix on Sunday but that is not what was planned.
Hamilton was spun round at the first corner by Vettel's Ferrari team-mate Kimi Raikkonen, but turned in a masterful display, and took advantage of two safety vehicle periods to finish behind Vettel.
The Englishman clearly blamed the Finn, who was handed a 10-seconds penalty, for the crash and found it hard to face Raikkonen or accept an apology.
Vettel also described how he had needed to "surprise" Valtteri Bottas for the manoeuvre at Brooklands that secured him, after a safety-car period, a dramatic Silverstone win.
In a thrilling race with two 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. "I had the advantage of the tyres, but it was not easy to find a way through". His team-mate Bottas, on older tyres, led the closing laps, but was unable to resist the challengers.
Raikkonen was eventually beaten by Hamilton but his own 10-second penalty did not actually drop him behind the Mercedes during the race.
It's more than likely a "heat of the moment" statement that perhaps Ferrari had any kind of plan to disrupt his race and that there was any link between what Raikkonen did and Vettel's contact with Bottas in France two weeks ago. Mercedes' errors cost both Hamilton and Bottas in the Austrian GP the week before when neither finished.
Hamilton made his way past Bottas on the following lap, with Raikkonen then taking his countryman for third, and that is how the leading four cars would cross the line in a frenetic ending.
"It was my mistake so that's fine, I deserve it". He was 19th and last, Brendon Hartley having failed to start in his Toro Rosso. It was still good enough to have a shot, so I gave it everything.
"This is the greatest race of the year and this is the greatest crowd and I'm sorry I couldn't bring it home for you today", Hamilton told his disappointed fans.