Brian Weatherall, 45, was driving along a misty lane in Kirkstone Pass with his family when the aircraft emerged unexpectedly from the fog, forcing him to hit the breaks.
Dash-cam footage of the incident shows the aircraft passing with within metres of his car.
After the helicopter disappeared from sight, Mr Weatherall can be heard saying to his family: “Dear me. That’s not something you see very often.”
It is thought that the aircraft was carrying out manoeuvres as part of an SAS operation.
“I just couldn’t believe it, I’ve never seen anything like it,” Mr Weatherall, a civil engineer from Durham, said. “I was on holiday at the time and the roads were bad so I was taking it steady on the steep hill. It happened about 2pm and I had the whole family in the car, it really was quite something – and a lucky escape.”
He added it had been “pretty awesome” to witness such an event. “It does make you feel safe when you see how our forces can fly a helicopter.”
British Special Forces refused to comment on the incident.