The Australian was back in 15th on the first lap, partly due to first-corner contact with Romain Grosjean, but primarily because he crawled away from his fourth place on the grid.
He ultimately managed to recover to second.
"I didn't have a clue what happened off the line," said Webber.
"We've had two or three good starts in the last few races and then the lights went out and we were back to our normal form...
"We need to have a look at why those pop up from time to time.
"Then I had Grosjean take my front wing out at the first corner.
"The boys did a fantastic job to replace the wing at the first stop and then my race could start from there."
Webber finished the race just 0.7 seconds behind winner Nico Rosberg.
"I would've liked more laps to catch Nico but he deserved the win," said the Australian. "He was strong all day."
Webber announced at the start of the British GP weekend that he would leave Formula 1 to join Porsche's new LMP1 programme after 2013.