Hamilton's second win of the season vaults the Briton to fourth place in the championship standings. Reuters Photo
Hamilton, the 2008 world champion who won from pole position
to chequered flag at the Hungaroring, wore a helmet with the words 'Go Team GB' and 'Go Team Grenada' on top with the two countries' flags on a yellow background.
Team mate Jenson Button, who finished in sixth place on Sunday, had the Union Jack painted on top of his helmet and 'Go Team GB' written on either side.
Button has more of an Olympic connection than Hamilton, with his performance engineer Tom Stallard winning a silver medal as part of Britain's rowing eight at the 2008 Beijing Games.
Britain 541-strong team is the biggest at the Games. Hamilton's paternal grandfather emigrated to Britain from the Caribbean island of Grenada, whose small team has never won an Olympic medal.
The 27-year-old Briton took control of the race from the start and stayed in front, pit stops apart, as he resisted strong late pressure to come home ahead of Finland's Lotus driver Kimi Raikkonen.
Hamilton's win was his second of the year and the 19th of his career.
Raikkonen pushed hard to find a way of passing Hamilton in the closing laps, but the Englishman resisted despite having to fight to preserve his worn tyres.
Raikkonen finished a strong second ahead of his Lotus team-mate, Frenchman Romain Grosjean, and defending world champion Sebastian Vettel of Red Bull.
Current world championship leader Fernando Alonso of Ferrari came in fifth.
Hamilton's McLaren team-mate Jenson Button finished sixth, while Bruno Senna in a Williams, Australian Mark Webber in the second Red Bull, Ferrari's Felipe Massa and German Nico Rosberg rounded out the top ten.
Alonso stays on top of the drivers' standings, but Hamilton closed the gap and his victory in the much improved McLaren boosted his team's hopes of mounting a challenge for the title in the second half of the season following the annual summer break.