Fortune can be a fickle mistress in Formula One.

Home hero Lewis Hamilton was dejected and apologetic after a mistake in qualifying but Silverstone rang with fans chanting his name as he fought back to win the British Grand Prix.

His victory was won at the expense of his Mercedes teammate and title rival Nico Rosberg, who retired with a broken gearbox.

The German had taken pole position and was leading at just over the halfway point before the pendulum of bad luck swung his way on lap 29.

It was the first time Rosberg has retired this season while, in contrast, Hamilton had failed to cross the finish line twice.

"Yesterday was a really difficult day," Hamilton, who was knocked back to sixth on the grid after choosing to pit rather than finish a final timed lap in qualifying, told reporters at the historic Silverstone circuit.

"I really had to pull up my socks and get on it. ... I felt I really let the fans, the team and myself down," Hamilton said.

Determined Hamilton

"Coming back today to turn that emptiness around was really my priority. This weekend showed you never give up," Hamilton said.

Hamilton's second British Grand Prix victory -- earned exactly six years after his fantastic 2008 win in the wet -- was not only about personal redemption, it was also about closing the gap in the F1 world championship.

Luck has been on Rosberg's side at the previous three races, the 29-year-old winning in Monaco and Austria and finishing second in Canada.

Hamilton's home win means he is now just four points behind Rosberg, who was still smiling as he chatted to reporters in the Mercedes motor home after the race.

The Mercedes duo will now renew their rivalries at the German Grand Prix on 20 July -- and Mercedes chairman Niki Lauda, a three-time world champion himself, is predicting fireworks now Hamilton is back to his best.

"Lewis from the beginning of the season was on a very good stable level and Nico after Monaco had everything going for him," Lauda said.

"But now Lewis is back on track so I tell you the next couple of races are going to be interesting," Lauda said.

Highly motivated

"He is highly motivated and for me the most important thing is that this victory gives him a real push about his qualities, what he can achieve so there will be no ups-and-downs with him anymore. Everything is reset like before. So they will fight until the end like you do not believe to be world champion," Lauda said.

There was also a turnaround in fortune for the Williams team, who saw their cars start out of position after failing to choose the right tires in a rain-hit qualifying.

Valterri Bottas hustled his way through the field with some impressive overtaking to finish a brilliant second in the car Susie Wolff had driven on Friday for four laps before it ground to halt with an engine problem.

"We're on the right way," said the Finn, who finished third last time out in Austria. "One step more to go.

"You see how quick the car is. It was a pleasure to drive. I was able to go through the field. I'm really, really happy."

Fine third

Daniel Ricciardo finished third for Red Bull Racing, the same position his teammate Sebastian Vettel had started the race from.

While the four-time world champion came in for fresh tires twice, Ricciardo switched to a one-stop strategy, which moved him onto the podium.

"I didn't intend on doing a one-stop but we were able to keep the pace, so we stayed on and just held on at the end," the Australian explained.