Fans huddling in the grandstands on what Red Bull team boss Christian Horner smilingly described as a typical English summer's day, with three seasons in as many hours, could only watch the rain falling steadily on an empty track for much of the second session.
Only after 51 of the 90 minutes had ticked away did a driver set a proper timed lap, with Toro Rosso's Spaniard Jaime Alguersuari at least giving the crowd some engine noise as he splashed around.
Massa, the fastest of the Ferrari drivers in the morning, set his best time of one minute 49.967 seconds right at the end of the session and on a drying track to topple Mercedes' Nico Rosberg off the top.
Webber, last year's winner at Silverstone, had been quickest in the morning with a best lap of 1:46.603 despite shutting down the engine and parking up on track at the end as a precautionary measure.
He was 14th after the break.
Seven-times world champion Michael Schumacher, who had told reporters on Thursday that he hoped for rain and got his wish, was second quickest for Mercedes in the morning and 0.660 off Webber's pace.
Reigning world champion and runaway title favorite Sebastian Vettel, who has won six of eight races to build up a 77-point lead over McLaren's Jenson Button and team mate Webber, was 13th and 18th respectively.
The main drama of the first session was provided by Japan's Kamui Kobayashi, who crashed his Sauber on the straight opposite the new pit and paddock complex with 15 minutes remaining.
The car was extensively damaged after it spun on the wet kerbs, pitched high and almost rolled on the runoff before smashing sideways into the tire wall. Kobayashi was third fastest in the afternoon.
Britain's hopes, McLaren's 2008 and 2009 world champions Lewis Hamilton and Button, were eighth and 15th respectively in the morning and fourth and fifth after lunch.
While Webber led the way early on, his compatriot Daniel Ricciardo was slowest on his debut for stragglers HRT but lapped quicker than Italian team mate Vitantonio Liuzzi in the afternoon.
Two Australians have not started a Formula One race together since Austria in 1977, when one of them — Alan Jones — was the winner.
The practice was the first since a clampdown came into force on the use of engine maps and exhausts to gain aerodynamic advantage.
Some teams may be more affected than others, given the different characteristics of the engines.
