A JK Rowling-backed petition calling for the Government to clarify equality legislation will be considered in Parliament after it received more than 100,000 signatures.

The Harry Potter author was among those to support the proposal which seeks to “make it clear” that “sex” and “gender reassignment” are separate protected characteristics.

Campaigners want to update the Equality Act 2010 to specify that “sex, male, female, man and woman mean biological sex” rather than “sex as modified by a gender recognition certificate”.

The group Sex Matters, in a briefing note, said: “Women (and men) face discrimination because of their sex. People often need different facilities and services based on sex.

“Organisations that provide single-sex services need clarity about the law. Single-sex associations, sports, charities and schools are also legitimate. All of this is allowed for by the Equality Act.

“Transgender people are protected from being discriminated against because they are transgender (through the protected characteristic of gender reassignment). This does not give them the right to override other people’s consent when it comes to their privacy, dignity and autonomy about sharing spaces with the opposite sex.”

After detailing what the amendment would do, it added: “Making this clear would resolve the uncertainty for women, transgender people, employers, schools and service providers. It would make it much easier to provide clear guidance and written policies that everyone understands.”

Liberal Democrat peer Baroness Ludford, speaking during the International Women’s Day debate in the House of Lords, said on Friday: “I believe we do need a change in the law.

“I support the petition organised by the organisation Sex Matters, which has been signed by 100,000 people and will therefore be debated in the other place (House of Commons), calling for reform of the Equality Act so that the protected characteristic of sex is clarified as meaning biological sex.

“It can apparently be done via the Gender Recognition Act, and it is not transphobic or bigoted to call for this legal clarification.

“Gender and sex have become conflated in popular parlance, probably because we were a bit coy about the term ‘sex’.

“The Gender Recognition Act uses gender and legal sex in the same section, but legally this has become very problematic, especially following a Scottish legal judgment which said that legal sex and biological sex are the same.

“This needs sorting out, and I hope the minister can assure us that the Government is attentive to this issue.”

Education minister Baroness Barran said: “The Government is clear: biological sex is a fact, it exists and it clearly matters.”

On Wednesday, Rowling wrote on Twitter: “If you’re concerned about the erosion of women’s rights in the UK – the right to single sex spaces like domestic violence refuges, rape crisis centres and prisons – sign the Sex Matters petition to make the Equality Act clear.”

Petitions which receive more than 100,000 signatures tend to be debated in the House of Commons’ second debating chamber, Westminster Hall.

Elsewhere in the Lords debate, Conservative peer Lord Shinkwin paid tribute to Rowling and other women for “standing up for equality”.

He said: “I refer to those who, while respecting trans people, nevertheless push back against the polarising poison of trans fanaticism, which tragically toxifies the vital debate on the essence of what it is to be human, especially in relation to our immutable biology.”