The Women’s Rights Network will launch a “coordinated series of actions” to ensure that anyone hoping for leadership understands their importance.
WRN spokeswoman Heather Binning said Mr Johnson recognized the importance of protecting same-sex spaces.
She said: “It is vital that the next Conservative leader – and the Prime Minister – does this too.”
Ms Binning added: “Women had to fight for the right to vote and, make no mistake, we will use our votes to defend our rights. Our members want clear, unequivocal assurances from all leadership candidates.”
WRN plans to ask each candidate about women’s rights.