By winning the British Grand Prix, Vettel became the first driver to win four races so far this season.
Hamilton's Mercedes suffered a hit from the Ferrari of Kimi Raikkonen on turn three of the opening lap at Silverstone, forcing him to the back of the pack from where he had to fight through the field to finish second behind Sebastian Vettel in the other Ferrari.
Hamilton can not afford a repeat of the botched start that saw him slip from pole to third where he was hit from behind by Raikkonen which cost him a victory and more vital points lost to Vettel. Hamilton, forced in to a spin, continued last on track, while Raikkonen was later deemed responsible by the stewards and given a ten-second penalty. Despite the fact that he started on pole, Hamilton wasn't able to take victory.
"I'm happy first of all for the team", the Italian told Channel 4. "We chose to go for the track position, it was the right call in my view, and we wouldn't have won the race otherwise in my opinion".
"And I want to remind everyone that, in China, we had a situation between Vettel and Verstappen and nobody said anything".
Hamilton was on a charge from the first lap, back up to seventh after nine laps but still 26 seconds behind his fellow four-times world champion.
The top six, now on the durable medium-compound tyre, settled into a rhythm, with Vettel leading Bottas ahead of Max Verstappen, Daniel Ricciardo and Raikkonen, but a lap-32 safety vehicle turned the grand prix on its head after Sauber's Marcus Ericsson had left his drag reduction system open as he entered turn one, crashing heavily into the barriers.
Onlookers observed that Hamilton looked angry when he got out of his vehicle at the end of the race, but the British star was quick to clarify his post-race demeanour when asked if he'd felt aggrieved.
Bottas, on old tyres, was starting to wane, and with five laps to go Vettel perfectly executed his move at Brooklands to take the lead.More news: Southgate in no mood to change England's winning formula
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"Thank you for loving me for being with all my flaws", said Hamilton, 33, on his Instagram account. "I will not give up, believe me, I will not give up", he said later.
"The team did an fantastic job this weekend, and we had so much support but also so much pressure", he said.
"Interesting tactics I would say from this side but we'll do what we can to fight them", Hamilton said.
"That's how it goes sometimes".
"It was my mistake". So I was nervous I had lost part of my floor or something because the auto was moving for unknown reasons, but then it started to get better and better, after some tweaks to the settings.
"I deserved it but kept fighting".
Bottas finished fourth, ahead of Daniel Ricciardo, Nico Hulkenberg and Esteban Ocon.
He was soon up to 16th and by lap nine he was eighth, but some distance from Vettel, who led Bottas by six seconds on lap 12. Meanwhile, Raikkonen was given a 10 second penalty for the collision with the British driver.