In an interview with Times Radio, to be broadcast at midday on Sunday, the 87-year-old broadcaster described the sexism she faced over her decades-long career at the BBC.
The Labour Party peer, who is a supporter of the MeToo movement, described being the “victim of unwanted attention” in the 1950s and 1960s.
“I was the victim of unwelcome attention all the time but so were all women,” she said.
Baroness Bakewell revealed an incident involving a junior government minister who had to be “fended off” after he grabbed her. The minister in question has since died.
"I was assaulted by a member of the government in a taxi when I went to fetch him from the House of Commons to come on the programme," she said.
"You know, this kind of thing happened. It happened all the time."
Responding to a question about whether she went to the police, the presenter said it would have been pointless, explaining: "They would've said, well, that's just to do with your private life, you're alright, he's not done anything that breaks the law."
The broadcaster, whose career spans over half a century, said there had also been a culture of sexism and harassment at the BBC.
She said it would have been futile to discuss harassment with senior members of the BBC "because they would be doing the same thing".
The journalist told of an attempt by a group of women at the BBC to file a complaint against a man who was later promoted “pretty near the top”.
"There was someone who was persistently harassing a whole department of women as it were, one by one," she said. "He would invite them home and behave badly and they began to tell each other.
"They began to share the secret with each other and found it hateful and so they decided that they would all get together and as a group make a protest about this person.
"And they went to the head of department and it eventually went up to, I think as far as the controller, and the person was reprimanded and then he was promoted."
The broadcaster said that although there were several predators at the BBC, nobody knew about Jimmy Saville at the time, but everyone thought he was “extremely weird”.
Baroness Bakewell has presented programmes including Late Night Line-Up and Heart Of The Matter.