Mr Johnson made the bizarre comment to Sir Drummond Bone in an interview for the Voices from Oxford website in 2013 after he was asked about his 2007 book on cars, Life in the Fast Lane.
“I think that women’s liberation – female suffrage – probably wouldn’t have happened, if it hadn’t been for the motorcar,” said the prime minister, who was then mayor of London.
“Basically because men realised that women were at the wheel of a machine that could run them down.”
Sir Drummond appeared to be sceptical of his claim and replied that he had never heard that argument before.
Mr Johnson, who did not seem to be joking, then explained his theory in more detail, noting that opponents of female suffrage in the 1890s warned against women using bicycles.
“They were so hostile to women on bicycles that they would hang bicycles from trees to indicate their displeasure that women were being able to use these liberating pieces of technology,” he added.
“But of course, when the combustion engine allowed women to travel at many miles an hour and to be in a position of command, I think the game was up.”
It is true bicycles played a role in emancipation as it helped bring greater independence to women’s lives.
Louise Jeye, a British writer, said in 1895 that there was a “new dawn of emancipation” being brought by the bicycle.
“The young girl of today can feel the real independence of herself and, while she is building up her better constitution, she is developing her better mind,” she wrote.
There was also opposition to women riding bikes, partly because some people worried the bicycle could cause sexual arousal in women.
However, it is not clear where Mr Johnson’s theory about cars came from.
“This is the latest in a long line of insulting and derogatory comments he has made about us.”
She added: “A Conservative government would spend the next five years cutting the services women rely on and creating more division in our society.”
In an article from 1995, Mr Johnson described the children of single mothers as “ill-raised, ignorant, aggressive and illegitimate” and referred to single mothers as “uppity and irresponsible women”.
In 2005, he wrote a column in which he suggested that the way to deal with advice from a female colleague was to “pat her on the bottom and send her on her way”.
The Conservative leader has also been criticised for saying Muslim women wearing burkas look like “letterboxes” and referring to gay men as “tank-topped bumboys”.
When Mr Johnson was confronted about his past comments on ITV’s This Morning, he said: “I don’t think this is the time to talk about articles written quite a long time ago.”
“People dig out all sorts of articles,” the prime minister added.
“I’ve already said sorry for any offence caused and I say it again.”
The Independent has contacted the Conservative Party for comment.