He was forced to swerve as the kilted crackpot played "chicken" on the Silverstone track.
Cars missed the 56-year-old Irishman by inches. He was waving a banner saying: "Read the Bible: The Bible Is Always Right."
Button said last night: "I was about to pull out and overtake when I noticed a madman on the circuit. It was a very scary feeling.
"I looked into his eyes and thought, `How weird is that? He does not care what might happen'. But we did.
"I was travelling at 185mph when I went past him. He would have felt the wind in his hair that's for sure."
"It does not bear thinking about what would have happened had he been hit.
"He would not have been the only one killed."