did their final preparations for qualifying at the British Grand Prix.
Hamilton beat Mercedes team-mate Nico Rosberg by 0.552 seconds, with the Ferraris of Kimi Raikkonen and Sebastian Vettel third and fourth.
Rosberg had a gearbox oil leak but it barely affected his running.
was a similar margin ahead on both types of tyres.
The Mercedes are well clear of the rest of the field – Raikkonen was 0.775secs behind Hamilton.
It was two-by-two through much of the top 10 around the fast sweeps of Silverstone, with the impressive Toro Rossos of Max Verstappen and Carlos Sainz Jr fifth and sixth, followed by the Williams cars of Felipe Massa and Valtteri Bottas.
Red Bull’s Daniil Kvyat and Lotus’s Pastor Maldonado completed the top 10.
A crowd of 105,000 is expected on Saturday and the grandstands and spectator areas were already packed as practice began at 10:00 BST in warm and bright conditions.
The fans’ hopes of seeing home success are dependent entirely on Hamilton, as Jenson Button had another difficult day with McLaren, ending 16th and 2.6secs off the pace.
Team-mate Fernando Alonso had an even worse time, managing only six laps before his running was ended by what is believed to have been a hydraulic leak.
a lead that has been cut by three victories in the last four races for the German.
The world champion had ended Friday practice off Rosberg’s pace and saying he would be “in trouble” if he could not improve the balance of his car, but he professed confidence before going to the garage on Saturday morning and was immediately quick when the Mercedes cars finally took to the track 15 minutes or so into the session.
Hamilton set the pace on his first flying lap on the hard tyre, beating Rosberg’s time by 0.037secs. Rosberg then took more than half a second off that before Hamilton beat him to be 0.398secs quicker on that tyre.
Rosberg then suffered a gearbox oil leak, but he still managed to get out before the end of the session.
By the time he did, Hamilton had posted a one minute 32.917 seconds lap on the ‘medium’ tyre that will be used for qualifying.
Rosberg was slower throughout the lap, 0.2secs off in the slow first sector, and 0.1secs off in the fast second, which contains the daunting Copse and Becketts corners.
Rosberg lost a further 0.2secs in the final sector, some of which may have been down to coming up behind a Toro Rosso into Vale.
Ferrari look a comfortable second, with Raikkonen responding to speculation about his future with a convincing showing so far this weekend.
And the strong high-speed downforce of the Toro Rosso car was paying dividends as they ended up ahead of the Williams cars, an impressive performance given that the Renault engine used by the Red Bull teams is at least 50bhp down on the Mercedes unit in the Williams.