Gay conversion therapy is abhorrent and has no place in a modern society, according to the health minister Norman Lamb, who has asked for assurances from NHS England that GPs do not make any referrals for such treatment.

"It is based on the completely false premise that there is something wrong with you if you happen to be gay," said Lamb, the minister for care and support. "I certainly want to do what I can, as a Liberal Democrat, to eradicate this."

Lamb spoke to the Guardian as 15 cross-party MPs wrote to him demanding tougher measures, including consideration of a ban on gay conversion therapy.

The minister convened a round-table meeting last week, to which he invited representatives of the Royal College of Psychiatrists as well as the gay pressure group Stonewall and others with concerns about counselling intended to help or persuade people attracted by the same sex to bury or eradicate those feelings.

There are no reliable, up-to-date figures on its use but a 2009 survey of 1,300 mental health professionals found that more than 200 had tried to help at least one client to reduce the attraction they felt for somebody of the same sex. A third (35%)were said to have been referred for therapy by a GP and 40% of those were reportedly treated within the NHS.

Lamb said: "I don't think there should be referrals to professionals in the NHS. I haven't seen evidence of referrals, but in a vast system [like the NHS] one imagines that could happen. So we have to be clear about the inappropriateness of that."

He has written to NHS England to stress that NHS money should not be spent in this way. "There are steps we can take to make sure it has no place in the NHS," he said. "We can also send a clear signal that health professionals within the NHS should not be referring people – it would be entirely wrong to make referrals."

Lamb did not consider a ban to be an option. "There will be people who want help with coming to terms with their sexuality and need to be able to seek support from a professional," he said. It was important to avoid a situation where a doctor or therapist felt they could not counsel someone in that situation. "We must not end up with a situation where we end up with people fearing they will be prosecuted."

Lamb has been under pressure from MPs and others to take a stronger stand, with calls for statutory regulation of psychotherapists, which could potentially enable disciplinary action against anyone involved in gay conversion therapy.

In a 30-minute debate in the House of Commons in November, the Liberal Democrat MP Stephen Gilbert said: "In the 21st century, no lesbian, gay, bisexual or transgender individual should be accessing this kind of voodoo psychology. Instead we should be providing services which help give them confidence and support them with their sexuality."

The Labour MP Sandra Osborne said: "Conversion therapy is a very real and present danger in Britain. More than just a problem amongst religious fundamentalists, it's an issue for the NHS and professional sector, and this isn't a simplistic debate about freedom to choose: if LGBT patients are coaxed into undertaking therapy by peer pressure or referred on to conversion therapists after approaching professionals, then this is hardly a 'free choice' at all."

Fifteen MPs of all parties have written to Lamb in the past few days, calling for the government to do more. They say it is not enough to warn health professionals against gay conversion therapy – they should be given training to help patients who come to see them with concerns about their sexuality, they say. NHS links with therapists who attempt gay conversion should be investigated and a ban to act as "a red flag" should be seriously considered.

"Now that marriage equality has been achieved, the LGBT community is rightly turning its head towards the broader forces underpinning inequality in Britain," says the letter. "If Britain takes bold moves against the practice here, there is also hope that it will go some way towards giving solace to the LGBT population in other countries who lack the most basic human right, and help rebuke an assumption that underpins much modern-day homophobia: that same-sex attraction can and should be changed."

The Labour MP Diana Johnson, one of the authors of the letter, was more critical. "The government just doesn't get it," she said. "This is not just an issue of wasting taxpayers' money to fund discredited conversion therapists through the NHS. The broader problem is that many doctors and therapists haven't received the proper training on what to do if a gay person approaches them about their sexuality and may end up informally referring them to people who will try to 'change' their sexuality.

"Dealing with this means measures such as training doctors and therapists properly and ensuring that the NHS only commissions therapists who are part of good professional bodies that have nothing to do with conversion therapy."