The famous hour markers have been fast for the past fortnight, interrupting BBC Radio 4 broadcasts that use the sound live.
The Houses of Parliament’s three dedicated clocksmiths have tried to deal with the problem by removing weights from the pendulum.
But they have no idea why it has happened, saying that at 156 years old the Great Clock just has “fits every now and then”.
Ian Westworth, one of the clocksmiths, told Radio 4’s PM programme: “The error started building up and went slightly unnoticed over a weekend.
“You cannot just wind the hands forward.
“You have to make a very gradual change by adding coins to speed the clock up or taking weight off to slow it back down again.
“We do not know why it happened.
“You are talking about a 156-year-old clock, it does have a little fit every now and then.
“It is a little temperamental.
“Imagine running your car for 24 hours a day, 365 days a year for the last 156 years.”
Initial attempts by the team to correct the mechanism made it run slow.
Mr Westworth said: “We have been up there most days just getting it right...
“Traditionally we have to go up three times a week to wind the clock.
“We phone up the speaking clock and at five minutes to the hour, start a stopwatch, go up to the belfry, stand by the bell and the hammer.
“As it strikes the bell we’ll stop the stopwatch.
“We can tell if it is going slightly fast or slow.”
Big Ben is the nickname of the Great Bell of the clock. The tower is officially known as the Elizabeth Tower, renamed as such to celebrate the Diamond Jubilee of Elizabeth II in 2012.