More than 100,000 people have signed an online petition calling for "conversion therapy" - aimed at changing a person's sexuality - to be made illegal.
It will now be considered for a debate in Parliament, having gained the required support, two years after the government pledged to ban the practice.
And the charity Stonewall has urged the government to "urgently" publish its plans to "end these harmful practices".
The government said it will "consider all options for ending the practice".
It added that certain "abhorrent and violent practices which may be classed as conversion therapy, such as 'corrective' rape" were already covered by existing criminal offences.
"Conversion therapy" refers to any form of treatment or psychotherapy which aims to change a person's sexual orientation or to suppress a person's gender identity.
Meanwhile, Liberal Democrat MP Layla Moran has tabled an early day motion - used by MPs to rally support for an issue - urging the government to ban the "outdated" and "harmful" LGBT "conversion therapy".
All major UK therapy professional bodies and the NHS disagree with it on logical, ethical and moral grounds.
The online petition, started by Mahed Asad, says of "conversion therapy": "The very thought of this sickens me, and I would like to see it stopped one day."
Josh Bradlow, policy manager at Stonewall, said: "Any form of 'therapy' that attempts to change someone's sexual orientation or gender identity is unethical, damaging and wrong.
"These so-called conversion therapies have been condemned by all major UK health organisations as they try to shame a person into denying a core part of who they are, and this can have a seriously harmful impact on their mental health and wellbeing."
Professor Wendy Burn, president of the Royal College of Psychiatrists, said: "Psychiatrists should be committed to reducing inequalities, not supporting practices that are explicitly based on pathologising LGBT individuals and their sexual orientation."
In 2018, it was announced that controversial "gay conversion therapies" were to be banned as part of a government plan to improve the lives of gay and transgender people.
At the time, the government did not offer a definition of "conversion therapy", but its report said it "can range from pseudo-psychological treatments to, in extreme cases, surgical interventions and 'corrective' rape".
A national survey of 108,000 members of the LGBT community suggested 2% have undergone the practice, with another 5% having been offered it.
Ms Moran, a Liberal Democrat leadership candidate who revealed in January she was pansexual and in a relationship with a woman, said she is calling on the government to make it a criminal offence to "force people to attend conversion therapy and to send individuals abroad for it".
"Conversion therapy is a deeply harmful and outdated practice," she said.
In response to the petition, the government called "conversion therapy" a "very complex issue".
"The UK government is committed to ensuring all citizens feel safe and are protected from harm," the statement said. "This is why we will work to deepen our understanding and consider all options for ending the practice of conversion therapy."
In January, minister for women and equalities Victoria Atkins said in a written statement that the government remained committed to the LGBT Action Plan, "including the commitment to end conversion therapy".
Last month Germany's parliament pass a law banning so-called "gay conversion therapy" - which claims to be able to change a person's sexual orientation - for under-18s nationwide.
The practice is outlawed in Switzerland and areas of Australia, Canada and the US.