A Fair Play for Women spokesperson has claimed legally allowing gender self-identification is "bad law".
Dr Nicola Williams, a spokesperson for the women's rights group, appeared on the breakfast show to discuss the Gender Recognition Act consultation, which ends today.
"They're proposing a crackpot idea that any man, trans or not, could change his birth certificate on demand - no checks, no doctors, no surgery. Just like that," Dr Williams told Julia Hartley-Brewer.
"That would be easier of course for trans people, but it's bad law, it's open to abuse."
'They've tried to bully us'
Dr Williams claimed Fair Play for Women's campaign to encourage people to reject changes to the GRA, which was introduced in 2004, had been an "epic David and Goliath battle" against the "powerful transgender lobby".
"You know what, we've won," she said. "They've tried to bully us and silence us so that they could push through this thing called sex self-ID without the public knowing.
"We've blown the whistle on them and the public are waking up."
Dr Williams claimed the Fair Play for Women's crowdfunded campaign had so far been "heartwarming".
"We're called a hate group. We've been running, I think, a really heartwarming campaign actually, where thousands of ordinary women have found the courage to stand up and actually just say no.
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"One woman baked a cake with our logo on and entered a WI baking competition."
She added: "If this law passed it would mean that a woman was someone that had a penis. I'm sorry but women do not have a penis and we must not have that written into law.
"I can have an opinion and so can other people, especially on something as fundamental as what a male and what a female is."
Moss Side campaign
Earlier this week, a campaigner for the group approached men in Manchester's Moss Side, encouraging them to join the campaign against the GRA consultation in order to "protect their daughters".
In a post on the group's official Facebook page said: "We spoke to taxi drivers, approached gangs of lads on their bikes. 100% support for women. 100% agreement that little girls’ safety matters most. Manchester men in Moss Side are very concerned to protect their daughters."
The move drew criticism online, with some transgender activists accusing Fair Play for Women of "incitement".
The group later released a statement online, which read: "Some activists have now accused her of some crime and she has been reported to the police! Why? Because her community is Moss Side.
"This is shameful stereotyping of a community, residents here also have the right to get information during a public consultation about a law change that could affect them.
"The silencing and intimidation of women speaking about their legitimate concerns is totally unacceptable and wrong."