Dame Jenni Murrayhas said that men who undergo sex change operations cannot be "real women", arguing many model themselves on a male view of what a woman should be.
The BBC Radio 4 presenter said that men who had grown up with all the privileges that entails did not have the shared experience of growing up female.
Murray's controversial remarks have received some backlash from transgender activists on social media, describing her comments as "divisive".
Jenni Murray of Woman's Hour: I'm not a transphobe or a TERF— Karen Cuthbert �� (@karencuthbert) March 5, 2017
Also Jenni Murray in same article: trans women are not women
The Woman's Hour presenter revealed that the first time she felt anger "when a man claimed to have become a woman" was in 2000, when the Rev Peter Stone underwent transition surgery and became Carol.
Murray said her impression of her meeting with Stone, just six years on from the first women priests, was that Stone's "primary concerns" were what to wear to meet parishioners and whether or not to wear make up.
"I remember asking Carol what she owed those women... His calling, as a man, had never been questioned. I had nothing but a blank look and more concerns about clothing," she said.
Murray said she was also incensed recently when she met India Willoughby, another trans woman who appeared on ITV's Loose Women.
Shocked to hear trans woman India Willoughby's comments dismissed by Jenni Murray with 'you've come to it fairly recently' #WomansHour— Hannah Silva (@HannahSilvaUK) December 2, 2016
Murray described her annoyance at Willoughby's belied that she was a 'real woman'' while ignoring the fact that she had lived most of her life "enjoying the privileged position in our society generally accorded to a man".
She also took criticsed Willoughby's agreement with the Dorchester hotel’s controversial code for its female staff - which asked that they always wear make-up, have a manicure and wear stockings over shaved legs, questioning whether the presenter was aware of the long-running debate on the topic among women.
"There wasn’t a hint of understanding that she was simply playing into the stereotype — a man’s idea of what a woman should be," said Murray.
It is not the first time the issue has stoked controversy - the feminist and writer Germaine Greer has previously been banned from speaking on panels following her suggestion that a post-operative transgender woman “can’t be a woman”.
Writing in the Sunday Times Magazine, Murray said she was not transphobic or anti-trans, adding that she was aware that her comments came at a time of bitter debate on the topic.
She said that she did not approve of the "extreme" statements that have been issued on the debate, saying that she did not agree with Julie Burchill or Germaine Greer whose language was "unacceptably crude".
She added that she was equally "appalled" at the misogyny shown by trans activists who demanded the “no platforming” (banning from speaking in public) of women "who have questioned the claims of trans women to be real women".
However Murray said she has found support among some transgender women, "who willingly accept they cannot describe themselves as women and who agree that sex and gender are not interchangeable".
Jenny Roberts, 72, who underwent surgery to change sex when she was around 50, told Murray: "A lot of trans women want to believe they are women, but we're not. We bring our male traits and habits with us."