The Mercedes cars were miles ahead of the rest of the pack at Silverstone and Hamilton was 0.228 seconds clear of the drivers’ championship leader.
Hamilton, however, did fail to complete a race-simulation run after his engine suffered an oil-pressure problem as he left the pits.
Ferrari’s Fernando Alonso was third-fastest ahead of Red Bull’s Daniel Ricciardo and Sebastian Vettel.
“The car felt good. It was just the most important run I missed,” said Hamilton.
“It happens. I don’t know why it happens to my car so much. I don’t really know what the car feels like for the race but I will try to get some long runs tomorrow.”
1. Lewis Hamilton Britain Mercedes-Mercedes 1m 34.508s 14 laps
2. Nico Rosberg Germany Mercedes-Mercedes 1m 34.736s 35 laps
3. Fernando Alonso Spain Ferrari-Ferrari 1m 35.224s 32 laps
4. Daniel Ricciardo Australia Red Bull-Renault 1m 35.511s 11 laps
5. Sebastian Vettel Germany Red Bull-Renault 1m 35.627s 27 laps
6. Valtteri Bottas Finland Williams-Mercedes 1m 36.016s 33 laps
7. Jenson Button Britain McLaren-Mercedes 1m 36.228s 34 laps
8. Kevin Magnussen Denmark McLaren-Mercedes 1m 36.299s 35 laps
9. Kimi Raikkonen Finland Ferrari-Ferrari 1m 36.554s 29 laps
10. Jean-Eric Vergne France Toro Rosso-Renault 1m 36.583s 26 laps
11. Felipe Massa Brazil Williams-Mercedes 1m 36.671s 29 laps
12. Daniil Kvyat Russia Toro Rosso-Renault 1m 36.778s 31 laps
13. Esteban Gutierrez Mexico Sauber-Ferrari 1m 36.951s 35 laps
14. Pastor Maldonado Venezuela Lotus-Renault 1m 37.064s 35 laps
15. Romain Grosjean France Lotus-Renault 1m 37.097s 33 laps
16. Sergio Perez Mexico Force India-Mercedes 1m 37.236s 37 laps
17. Nico Hulkenberg Germany Force India-Mercedes 1m 37.449s 27 laps
18. Adrian Sutil Germany Sauber-Ferrari 1m 37.520s 25 laps
19. Jules Bianchi France Marussia-Ferrari 1m 38.658s 11 laps
20. Kamui Kobayashi Japan Caterham-Renault 1m 39.068s 31 laps
21. Max Chilton Briton Marussia-Ferrari 1m 39.224s 28 laps
22. Marcus Ericsson Sweden Caterham-Renault 1m 39.762s 21 laps
MORE: The latest football news
MORE: The latest tennis news