Since it began in 1946, Radio 4’s Woman’s Hour has been singing about women’s successes, shouting about their struggles and interviewing the good and great along the way. It has become an institution, along with its formidable presenter for the past 30 years, Jenni Murray. Now, a book has collected the wit and wisdom of the show’s most prominent guests, many of whom Murray interviewed with her distinctive blend of disarming warmth and unnerving directness.

There was the time when she asked Hillary Clinton why she had stayed in her marriage despite its humiliations. And the time she asked Monica Lewinsky why she had kept “that dress”. She’s had conversations with nearly every significant woman of the past 70 years, from Margaret Thatcher and Aung San Suu Kyi to Angelina Jolie and Nicole Kidman.

Today, at the age of 66, Murray is still going strong. We speak on the phone just before her controversial comments on transsexuals are published in a Sunday paper.

It is hard to picture Murray as scared of anyone, but she remembers the first time she really got nervous was in 1987, two years into the job, when she had to interview Bette Davis. The 81-year-old was “stunningly dressed and perfectly made up”. Murray had just read her autobiography, which described how Davis had made meals for servicemen during the Second World War, so she began the interview by asking her about that rather than the obvious questions about her acting career. “It worked a miracle and she was putty in my hands.”

Her second interview with Clinton in 2014 had a bumpy start. She came in just as Murray was finishing off an interview with Shirley Williams and sat in the seat that Williams had just vacated. “She then picked up a handbag and slapped it across the table. I thought, ‘Good grief, is Hillary Clinton throwing a handbag at me?’”

It turned out that Williams had forgotten her handbag in the studio and Clinton didn’t want her to leave without it. “In those few moments, I knew she was one of us – she knew that the handbag held a life support system,” says Murray.

Clinton went on to give her “the most fabulous interview. When I asked her why, when her husband had humiliated her on so many occasions, she had remained with him, she spoke of marriage being a friendship, not necessarily about sex. She said, ‘When we met we were at university, where we started a conversation. We are still having that conversation.’”

Did anyone disappoint her? “No,” Murray says. “The people who are really top-ranking make the effort to give the very best of themselves.” Oprah Winfrey was a case in point. “She didn’t make any bones about her weight going up and down. She said, ‘What kind of a life is it without a French fry ever?’” Murray can relate to that: “I had the same problem that she had, going up and down, until I had stomach surgery [in 2015].”

There have been awkward interviews, too. Margaret Thatcher “had these blue eyes that bore into you”. There was a particularly uncomfortable meeting with her in 1993 after she had been ousted as prime minister. Murray asked how she had dealt with sexist comments, such as Alan Clark’s reference to her “pretty ankles”, or François Mitterrand saying she had “the eyes of Caligula and the lips of Marilyn Monroe”.

“She looked at me and didn’t speak,” remembers Murray. Much later, it struck the presenter that out of protectiveness, Thatcher’s press secretary might not have shown her every newspaper cutting about her, and that “when I put those things to her, she was genuinely shocked”.

Murray has shared her own experiences with listeners, when she felt it necessary; the most important instance of this was in 2006 when she was diagnosed with breast cancer. “I knew I had to talk about it. I couldn’t just disappear to have a mastectomy… You develop a closeness to your audience and we had done so much on breast cancer on the programme. So I talked about it and so many women said they were very grateful for it.”

After three decades of flying the flag for women, and feminism, does she feel significant progress has been made? “When I recently interviewed Stefanie Martini, [the star of the Prime Suspect prequel set in 1973], it made me think about the early 70s when a woman police officer wore a skirt so she couldn’t run and a hat that didn’t give enough protection. Some things have changed infinitely for the better. But what we’re not even beginning to sort out is the childcare problem. And there is also domestic violence, which simply has to be stopped.”

 For all its acclaim, Woman’s Hour has had its detractors, too, who have called for a “Man’s Hour” (which they got last year on Radio 5 Live). There was also Piers Morgan who recently called for a “men’s march” after women protested around the world in January. What does Murray think about that? “It’s up to them. They can talk or march for whatever interests them. As long as they don’t mock us.”

Woman's Hour is on BBC Radio 4, Monday to Friday at 10am; Weekend Woman's Hour is at 4pm on Saturdays