Britain's leading body for Christian therapists has instructed its members to stop trying to turn gay patients straight using so-called "conversion therapy".

The Association of Christian Counsellors (ACC) said the practice should be stopped "in the interests of public safety", but the move has prompted a furious response from proponents of talking "cures" for homosexuality who have promised to fight for what they see as the right to therapy of anyone distressed by "unwanted same sex attraction".

The controversial practice seeks to unearth childhood traumas, which are considered by conversion therapists to have caused homosexuality. Sexual abuse, bullying and having an overbearing mother or distant father are among the supposed triggers.

Research by the US clinical psychologists Ariel Shidlo and Michael Schroeder has shown such treatment routinely led to worsened mental health, self-harm, thoughts of suicide and suicide attempts.

The decision by the ACC to speak out against the practice follows similar statements in the last two years by the British Association for Counselling and Psychotherapy, the UK Council for Psychotherapy and the Royal College of Psychiatrists and the Department of Health.

The ACC said the treatment, also called reparative therapy, "implies that sexuality can be 'repaired' and so introduces the idea of treatment or cure … it suggests that a specific outcome is possible and appears to make an a priori assumption that it should happen".

The statement makes it clear that the practice is incompatible with the Equality Act 2010 and it is not endorsed.

However, one organisation preparing to resist the ruling is the Core Issues Trust, a Northern Irish group that campaigns for Christian therapists who attempt to "treat" homosexuality and whose 2012 adverts stating, "Not gay! Ex-gay, Post-gay and Proud. Get over it!" were prevented from appearing on London buses by Boris Johnson after the Guardian alerted the mayor.

In an online statement rebuking the ACC's position, the Core Issues Trust said it was "a misapplication of Equalities Act 2010 [sic]", demanded the ACC "provide empirical evidence to support its misleading statement produced on the matter of counselling same-sex attracted persons" and urged the organisation to "avoid compromise of its members' right to teach and uphold orthodox Christian sexual ethics".

Other therapists are also preparing to lobby against the ACC's new stance. Lesley Pilkington, who has been on the ACC register, became the first psychotherapist in history to be "struck off" after practising conversion therapy. In 2012, after her methods were exposed, the British Association for Counselling & Psychotherapy (BACP) revoked her membership, finding her guilty of "professional malpractice", but she was able to join the ACC as counselling and psychotherapy remains unregulated by statute.

In emails from Pilkington seen by the Guardian, the disgraced therapist said there was "a fight going on", adding, "I believe that if anyone is distressed by their unwanted same sex attraction they should have the right to help and therapy … I will be releasing my own statement soon."

The ACC justified its new stance – a change since their its last statement in 2012 – explaining "such models have the potential to create harm and therefore [we] view them as incompatible within the ethos of counselling".

It advised members not to "commence or continue" using such methods and to remove or modify any promotional material advertising such a service, adding: "In the interests of public safety, we have decided to make clear what is expected by those who choose to be part of ACC."

The second reading of the counsellors and psychotherapists (regulation) bill, introduced by the Labour MP Geraint Davies in an attempt to combat conversion therapy and introduce statutory regulation, will be heard on 24 January. A conference for conversion therapists will take place in London on 16 January.

Britain's most senior psychiatrist applauded the ACC's position. Professor Dinesh Bhugra, incoming President of the World Psychiatric Association, told the Guardian: "I welcome this major step forward. I very much hope any other organisations who have not already done so follows suit to save a lot of false hope and pain. Psychotherapists and counsellors should focus on supporting individuals to accept normal human variation."