All of the teams carried out a timed lap in the afternoon session following the earlier practice, in which just 11 drivers took to the circuit due to puddles of water covering the track.
Red Bull's Sebastian Vettel was quick out onto the Silverstone circuit with intermediate tyres at the start of the second session after the wet weather cleared up.
However, it was Rosberg who clocked a time of 1:32.248, while Mark Webber secured the second-fastest time in his Red Bull, with teammate Vettel placing the third quickest.
Lewis Hamilton, who was the last Brit to win the race in 2008, managed to claim the fifth-quickest time out on the track, which managed to escape further rain.
Despite the drier conditions, the session didn't finish without some controversy as Felipe Massa smashed the nose of his Ferrari into the wall due to his cold tyres and too much throttle.
Second practice full standings:
1. Nico Rosberg (Mercedes)
2. Mark Webber (Red Bull)
3. Sebastian Vettel (Red Bull)
4. Paul di Resta (Force India)
5. Lewis Hamilton (Mercedes)
6. Daniel Ricciardo (Toro Rosso)
7. Jean-Eric Vergne (Toro Rosso)
8. Adrian Sutil (Force India)
9. Romain Grosjean (Lotus)
10. Fernando Alonso (Ferrari)
11. Jenson Button (McLaren)
12. Nico Hulkenberg (Sauber)
13. Kimi Raikkonen (Lotus)
14. Sergio Perez (McLaren)
15. Esteban Gutierrez (Sauber)
16. Valtteri Bottas (Williams)
17. Pastor Maldonado (Williams)
18. Jules Bianchi (Marussia)
19. Giedo van der Garde (Vaterham)
20. Charles Pic (Caterham)
21. Max Chilton (Caterham
22. Felipe Massa (Ferrari)