When the Women and Equalities Committee published a report calling for a sea-change in attitudes to transgender people, Maria Miller, the chair of the committee, might have expected to be attacked by right-wingers within her own party.

But, while they were largely silent on the issue, the former Culture secretary said she was taken aback by the “extraordinary” hostility from a minority of women “purporting to be feminists”.

Speaking to The Independent on Sunday from her office in Westminster, Ms Miller insisted that the “overwhelming” reaction to her report has been positive. Despite controversial calls for “gender neutral” passports and for 16-year-olds to be given the legal right to change their sex, there was barely a peep from her more traditional colleagues on the Tory back benches.

“The only negative reaction that I’ve seen has been by individuals purporting to be feminists,” Ms Miller said. Many are furious with her call for women’s refuges to ensure equal access to people who have transitioned from male to female.

A glance at Ms Miller’s Twitter page shows that the backlash is real. She is accused of exposing women to “violent men hiding behind the mask of transgender”. In another message, she is told trans women are “not real women” and are often “violent offenders or sex offenders” and that she was failing in her duty to protect women.

It follows on from Germaine Greer’s remark that transgender women “can’t be women”, adding: “Just because you lop off your penis … it doesn’t make you a woman.”

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But Ms Miller, wading into the dangerous territory of radical feminist politics, insisted that they are wrong. She pointed to research by the Fawcett Society, a think-tank campaigning for women’s rights, which found that two-thirds of feminists believe gender to be fluid. “Of course, that would cut across what Germaine Greer is saying,” she said.

“I think that all of us who are feminists know that equality for other groups of people, and a fairer deal for other groups of people, is good for us as well. If we live in a fairer society, where opportunities are not cut off because of your gender or sexuality or race or religion, then that is going to be good for women as well as good for everyone else.

“We should all be fighting for a fairer society. I find it extraordinary that somebody wouldn’t acknowledge that. But there seems to be an undercurrent of opinion among some that trans people shouldn’t be treated equally, even when they’ve had a legal change in their gender, and that in some way this is a threat to women; I simply reject that.”

She praised the “important work” of single-sex services, such as rape crisis centres. “But those sorts of services should be supporting trans women,” she insisted.

Ms Miller’s fellow committee member Jess Phillips, the Labour MP who ran a rape crisis centre before entering Parliament, admitted she could “understand” the concerns raised by some women.

“Some feminists prioritise gender equality above all else, but I think we should also do our bit to promote general equality,” she said. “I’m not upset with the backlash, but we’re all much better off when we are all better off.”

“We will only achieve equality if we push things forward – we just need to put in the safeguards. Some feminists take a different view. But I would prefer it if these trans people didn’t face dark and twisty childhoods. If there is anything I can do to stop that, then I will – even if it rubs a few people up the wrong way.”

Back in Ms Miller’s Westminster office, decorated with pictures of her family and an award from Pink News for “MP of the Year”, the MP admitted being surprised that more people had not been “rubbed up the wrong way” by her report – particularly by the criticism levelled at the NHS over its “shocking” treatment of transgender people.

The fact that an individual seeking a recognition of their legal change in gender has to be diagnosed with a mental health condition first “shows how far we have got to go with this issue”, she said.

To have your gender changed legally, transgender people also have to provide evidence of “living in your new gender”. “What does that mean in 21st-century Britain? That you wear a skirt?”

The one area of the health service which is “particularly” concerning is the lack of support from some GPs. Ms Miller has called for a “sea-change for how trans people are supported within the NHS”.