A Christian charity which sponsored a conference promoting the idea that gay people can be converted to heterosexuality has funded interns for an estimated 20 MPs, including some who are now ministers in the coalition government.

The Christian Action Research and Education charity (Care) has provided staff to the parliamentary offices of Caroline Spelman, Alistair Burt and Steve Webb. In 2009 it sponsored a London conference about homosexuality and Christianity which included sessions on "mentoring the sexually broken". The event in London was also organised by Anglican Mainstream, one of the conservative Christian charities that was blocked this week from showing adverts on London buses that supported the idea that with therapy, homosexual people can become "ex-gay".

The conference featured a keynote by Joseph Nicolosi, a Californian psychologist and founder of the National Association for Research and Therapy of Homosexuality. The organisers said they were "very worried about the continued progress of the gay – and in fact the LGBT – agenda across the board in the UK. Social, cultural, political and religious sectors are being targeted and most of them are capitulating".

MPs involved in accepting assistance from Care under its educational leadership programme are now facing pressure to sever their ties with the charity. None of Spelman, Burt or Webb were available for comment.

"It's a complete disgrace that any elected representative would have associations with an organisation that promotes a 'gay cure' in the 21st century," said Phillip Dawson, who launched a campaign when he discovered his local MP, David Burrowes had an intern sponsored by Care. "The Royal College of Psychiatrists has explicitly stated that discussions of a 'gay cure' fuel discrimination and prejudice. MPs should be fighting homophobia wherever it occurs but by associating themselves with Care they are actually helping to fuel it. We have to be clear that there is no place for groups that promote a 'gay cure' in the corridors of power."

The register shows that Spelman, now secretary of state for the environment, declared an intern sponsored by Care from 2007 until July 2009. Both Burt, a Foreign Office minister, and Steve Webb, pensions minister, declared they had interns sponsored by the charity between October 2009 and July 2010. Each of them estimated the value of the support to be £8,880.

Care has said interns on its leadership programme are not involved in lobbying. The Rev Lyndon Bowring, the organisation's executive chairman, wrote in a foreword to the internship scheme's latest brochure: "Christian graduates are given the opportunity to explore how to live out their faith as they meet and learn from leaders in the public arena; and actively engage in the world of policy whether in Westminster, in Edinburgh, in media or in the third sector."

A spokesman for Care said the programme was "a well-respected training initiative for Christian graduates". Asked about the organisation's belief in reparative therapy for gay people in the church, he said: "If there are people who want to change their sexual behaviour or orientation, who have an unwanted same-sex attraction and voluntarily seek help, there is no reason why they should not be at liberty to do so."

Care interns are currently recorded for Conservative MPs John Glen and Gary Streeter, Labour's Sharon Hodgson and Catherine McKinnell and the Lib Dem president Tim Farron. The register for the 2009-2010 parliamentary session shows that the Lib Dem MP Alan Beith and the former Labour MPs David Drew and Andrew Reed also employed Care interns.

Some MPs who employed interns from Care, including Labour's David Lammy, have already cut their links with the charity. Farron has told Care that he will not employ another of their interns because, he said on Friday night, "I don't agree with the idea of a gay 'cure' and I think it is grossly offensive, homophobic and wrong. It shows the church in such an awful light."

Catherine McKinnell said she was deeply concerned to hear about the event that Care part-funded in 2009 and immediately made a decision to terminate the intern arrangement. "I will not be taking any Care interns in future," she said.

Sharon Hodgson said she had also announced that she would no longer be accepting interns from Care. "The theories discussed at the conference in question could not be further from my opinion, and my voting record on gay rights speaks for itself," she said.

The extent of the internship programme's reach inside Westminster provided fresh evidence of conservative Christian organisations' desire to address what they feel is an increase in secularism. On Thursday an attempt by Anglican Mainstream and Core Issues Trust to run adverts on London buses promoting the possibility of gay people using therapy to change their sexual orientation was stopped by the London mayor, Boris Johnson. Anglican Mainstream said on Friday it had instructed a lawyer to prepare action against the mayor and CBS Outdoor, the company that booked the adverts, unless they reverse their decision.

"It is of deep concern that there can only be one point of view and that is the point of view of individuals who are determined to push through gay marriage and apparently believe that homosexuality cannot be altered in any possible way," said Core Issues' co-director Mike Davidson. "That is not a universally held view. This is a disturbing development and it is disappointing the UK finds itself in this position."

In January, Core Issues staged conferences in Belfast and London backed by Anglican Mainstream, entitled The Lepers Among Us. The lead speaker was Dr Jim Reynolds, an evangelical preacher from the US, and the programme explained that homosexuality, or as he it put it "same-sex sin", is "a disease of epic proportions, a malignancy that spreads". Sessions included "naming the sin, lifting the shame" and "normal sinfulness or a sickness". The event drew protests from gay groups appalled by the title and the content of the conference.

Speaking at the event at Belfast's Orangefield presbyterian church, Reynolds said of gay rights protesters: "We disagree about the fact they want to live their life in a homosexual relationship and we do not think that is the will of God."

Jeremy Marks, founder and director of Courage, a Christian group that supports same-sex partnerships, said: "I find some of Anglican Mainstream's messages and the way they set about things to be extremely offensive and unpleasant.

"They are marginal in the Christian community but they have a lot more influence than their size suggests."

• This article was amended on 16 April 2012 to add quotes from Catherine McKinnell and Sharon Hodgson which make clear that they have cut ties with Care. The article was further amended on 17 April 2012 because the original said that the Lib Dem MP Alan Reid had used a Care intern. He has never done so. The reference should have been to the former Labour MP Andrew Reed.