The incident at Turn 3, which saw Raikkonen collide with the Briton sending him into a spin which dropped him to last, follows a similar clash in France in which Vettel hit Valtteri Bottas at the first corner.
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.
It was Ferrari's first win in Britain since 2011.
"I think my car's broken", said the defending champion as he reconciled himself to a charge through a field shaken by the opening lap incidents.
When provided with the right to reply, Vettel wryly retorted: "Things can happen, but I think it's quite silly to think that anything that happened was deliberate".
Unexpectedly, Ricciardo made a second stop after 31 laps, lifting Hamilton to fifth as the Australian rejoined sixth, but on softs.
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 auto.
"Dead last to P2, that's an awesome effort", Mercedes told Hamilton.
Vettel passed Bottas at Brooklands five laps from the end, with the Finn's tires fading, and Hamilton was also through a lap later and the chase was on to the finish with the German winning by 2.2 seconds. I will not give up.
"My team did an fantastic job this weekend", said Hamilton, when he was, eventually, interviewed on the podium and after the two Ferrari men had departed.
Expanding further in the press conference, Hamilton said: "All I'll say there's now two races the Ferraris have taken out one of the Mercedes". The current F1 champion is now eighth, while Raikkonen receives a 10-second penalty for causing the collision.
"That's how it goes sometimes. Without the mistakes and the penalty it would have been better, but I tried".
The Red Bull pairing of Dutch 20-year-old Max Verstappen, victor in Austria last weekend, and Australian Daniel Ricciardo qualified fifth and sixth.
He fell to 16th but recovered to second, ahead of Raikkonen who completed the podium.
Elsewhere, solid drives from Fernando Alonso and Nico Hulkenberg pushed them level with Force India in the points table.