Pink News reports:
The body met in Brighton yesterday and more than two-thirds of doctors present backed a call for the Royal College of Psychiatrists and other mental health standard-setting bodies to reject the treatments and ban their use in codes of practice.
Health departments should also investigate alleged cases of conversion therapy being funded by the NHS, the meeting agreed.
Research published last year found that a sixth of registered British therapist and psychiatrists have attempted to "cure" patients of homosexuality.
Tom Dolphin, the proposer of the motion and the vice-chair of the BMA's junior doctors committee, said: "Sexuality is such a fundamental part of who a person is that attempts to change it just result in significant confusion, depression and even suicide.
"You can’t just wish away same-sex attraction no matter how inconvenient it might be."
But Cardiff consultant neurophysiologist Gareth Payne said there was no "gold standard" evidence that conversion therapy did not work and was harmful.
He added that it was important to respect the wishes of patients who asked for the therapy.
Earlier this year, gay journalist Patrick Strudwick published an expose of 'ex-gay' therapists and began a campaign group to persuade medical bodies to condemn the treatments.
He went undercover for the article, telling two therapists he was struggling to cope with attraction to men and wanted to be straight. One therapist, named only as Linda, tried to convince him he must have been sexually abused as a child by a member of his family.
The other, who PinkNews.co.uk later revealed was homophobic former Northern Ireland MP Iris Robinson's advisor, tried to make Mr Strudwick sexually aroused during his therapy.