Grosjean's early time of 1:18.218 wasn't headed, although the French driver did stop out on track during the dying moments of the session.
Paul di Resta was second in the Force India, ahead of the Toro Rosso of Daniel Ricciardo.
Mark Webber, in fourth, was the only driver to run for more than a hundred laps as he ended the day on 101.
Nico Hulkenberg was fifth in the Sauber C32, who also stopped on track towards the end of the day.
It was another dismal day for Mercedes. After Nico Rosberg's running on Tuesday was curtailed after fourteen laps with an electrical fault, a mechanical failure on Wednesday pitched Lewis Hamilton into the wall at Dry Sac. The 2008 world champion had completed only fifteen laps and did not emerge again as Mercedes tried to understand the issue.
Sergio Perez made his McLaren debut by finishing seventh. The team spent the afternoon focusing on long runs.
Felipe Massa was eighth, ahead of Pastor Maldonado in the Williams FW34.
Giedo van der Garde was tenth, just over three seconds behind Grosjean.
Luiz Razia made his début for Marussia around an hour after he was announced as a 2013 driver with the team. The Brazilian stopped on the pit straight after thirty laps of running and ended the day at the bottom of the timesheets, over five seconds off the pace.
Force India simulator driver James Rossiter conducted the final hour of running for the Silverstone based team as they attempt to get an improved benchmark for their simulator.
Several driver changes take place for Thursday's test as reigning world champion Sebastian Vettel gets his first run in the Red Bull RB9, as does Kimi Raikkonen in the Lotus E21. Jenson Button and Nico Rosberg also return, with Jean Eric Vergne, Esteban Gutierrez, Valtteri Bottas and Charles Pic also being given their maiden 2013 runs.