Nimco Ali claimed the Health Secretary found her via a Google search and that he had no idea about FGM at the time.
The former civil servant, who is the director of the Daughters of Eve non-profit organisation, told the News Roast podcast that the pair met at his Whitehall office four years ago.
“This man is the Secretary of State for Health but he has no idea about FGM and I don’t think he even reads his briefings,” said Ms Ali, recalling her thoughts at the time.
She added that he probably got in touch after reading a newspaper article about the subject, "so then he ‘googled’ and found me."
She said: "So I got an email to say ‘will you come in and speak to the Secretary of State and I said ‘yes’ because we need data and the NHS is, like, right at the forefront.
After waiting in his office, Ms Nimco said he walked in "rolling up his sleeve, and said he just did a night shift for the hospital."
Then she said he asked: "What I really want to know Nimco, is, can girls like you have an orgasm?"
She said: It was his first direct question. My reply was: ‘Well, it depends how good you are Jeremy. Because 80 per cent of the clitoris is actually internal, but let’s move’.”
News Roast presenters Heydon Prowse and Jolyon Rubinstein called his question “disrespectful” and “crude”.
But Ms Ali replied: “I think he is privileged enough to ask those questions.”
Asked if the two then started dating, she said: “I have boundaries.”
Ms Ali went on to praise the former under secretary for public health, Jane Ellison, for her campaigning on FGM.
An FGM survivors’ ability to have an orgasm depends on the type of FGM and cutting they have suffered.
Mr Hunt’s health department has since started publishing annual statistics for FGM and the latest data revealed nearly 5,500 new cases in 2016.
Met Police inspector Allen Davis last month said the force still did not know where in the UK FGM was taking place.
The Department of Health refused to comment on Ms Ali's allegation.
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