The six-time gold medallist was competing in an event at the famous Silverstone race track in Northamptonshire when he lost control of the car.
His Caterham Seven - a super lightweight sports car - veered off the Formula One track after its accelerator jammed before smashing into a tyre barrier.
Sir Chris said his brain "rattled around like a pea in a whistle" after his head was painfully jolted back by the force of the collision.
The 43-year-old, from Edinburgh, posted footage of the dramatic incident online, which was captured by the car's on-board camera.
It shows him reaching a top speed of 125mph before the throttle on the car jams open, leaving him unable to slow down turning into the corner.
He is seen desperately trying to slow the vehicle down, before careering off the circuit into a gravel trap and hitting the barriers.
Amazingly, he escaped unscathed from the crash and went on to compete in another two races.
He said online: "When the throttle pedal sticks fully open going into the fastest corner on the track.
"Thought I'd locked up so came off the brake only to feel the car accelerate.
"Scared the bejeezus out of me though when the brakes did nothing to slow it down. My wee brain rattled around like a pea in a whistle.
"All ok though, scary experience to feel the car keep pushing on towards the wall."
After he posted the footage on Instagram, his wife Sarra, 39, replied: "Good god. There’s no way I’m liking this."
Sir Chris was competing in the Caterham Seven 420R Championship at Silverstone over the weekend.
He became one of the country's most famous sportsman after winning three golds at the 2008 Beijing Olympics.
He claimed six Olympic gold medals in total - including two at London 2012 - before retiring in 2013.
However, he has since launched new careers as a professional racing driver and a children's author.