Mercedes' Lewis Hamilton celebrates on the podium with the trophy after winning the British Grand Prix. Photo: CFP

Lewis Hamilton won his home British Grand Prix for the third year in a row on Sunday with Mercedes teammate and title rival Nico Rosberg finishing second but under a stewards' investigation.

The triple Formula One world champion's fourth home win, from pole position in tricky conditions, was the 47th victory of his career and cut Rosberg's overall lead to four points after 10 of 21 races.

Rosberg was slowed by a gearbox problem five laps from the end and crossed the line 6.9 seconds behind, with a ­question mark over his result after Mercedes seemingly broke the rules on radio advice by telling him to avoid seventh gear.

Red Bull's Dutch teenager Max Verstappen was third, 1.3 seconds behind Rosberg, in a race that began behind the ­safety car after heavy rain ­before starting properly at the end of the fifth lap.

"I don't know if you can be as happy as me but I'm ­really happy," Hamilton told the 130,000-strong crowd that stood and cheered him all the way round the final lap with the sun shining brightly at last.

The Briton got even closer to the fans, who flooded onto the track, after parking up at the finish, and then enjoyed some celebratory crowd-surfing after the podium presentation.

"I'm glad that the good English weather came out. It was so tricky in those conditions. When we started the race, I was the first one who had to attack it," said the champion.

"It's never plain, smooth sailing - that's why the British GP is the best."

Hamilton is now the closest he has been to Rosberg this season and that gap could narrow even further if stewards rule Mercedes erred in telling the German what to do.

Red Bull principal Christian Horner said the radio rules were "pretty clear" and questioned where Rosberg, who was booed by some in the crowd as he stepped onto the ­podium, would have finished had Mercedes not given him their ­advice.

But Mercedes team boss Toto Wolff said the governing FIA would have to decide.

"We know what is allowed on the rules. The gearbox was about to fail. We think we should be OK, but we'll wait," the Austrian told the BBC.

Rosberg, who had a stirring battle with Verstappen that involved each overtaking the other, said he was confident the team had acted within the rules.

Australian Daniel Ricciardo was fourth for Red Bull, 17.9 seconds behind his team mate, with Ferrari's Kimi Raikkonen fifth.

Mexican Sergio Perez was sixth for Force India, with team principal Vijay Mallya able to attend a race for the first time this season, having previously had his passport withdrawn, with German team mate Nico Hulkenberg seventh.