Ms Bergman joined the scientist on the show to debate whether IVF – a medical treatment pioneered by Professor Winston – should be offered as part of the NHS.
It comes as local NHS cuts force 13 areas of England to stop offering IVF treatment to infertile mothers.
Ms Bergman said: “I think it’s something that I feel very strongly about, the NHS is woefully underfunded we all know that.
“The NHS exists to keep us healthy, IVF isn’t a cure to an illness it’s a solution to people who feel they are not achieving their life goals and I don’t think that is the responsibility of the NHS.”
It comes as local NHS cuts force 13 areas of England to stop offering IVF
The professor responded by asking “Serena, have you had children?”, with the journalist claiming she did not see “how that’s relevant”.
Professor Winston said: “No, it’s very relevant. It’s very, very relevant and I’ll explain why it is relevant.
“But you don’t have to answer the question and I don’t mean to be in any way discourteous to you.
“I’ve published hundreds of scientific papers, and you have very kindly called me a pioneer of IVF which is probably an exaggeration, but you know of all my achievements, my three children are the things that changed my life.
When a cis man starts an argument about pregnancy with “do you have kids?” and you’re like “do you have a womb?!”
— Sirena Bergman (@sirenabergman) August 7, 2017
“They are the most important aspect because they are the next generation and that is what we can contribute to.
“And people who are infertile suffer hugely, they suffer the pain just the same as somebody with an arthritic hip or knee do.
“At the moment this is not being fully understood and…