Lib Dem leader Tim Farron has denied that he told gay MPs he would pray for them, in a fierce exchange with gay Tory MP Ben Howlett.

Mr Farron, who last year replaced Nick Clegg as leader of the Liberal Democrats, is a devout Christian with a mixed voting record on LGBT rights – though he is now an outspoken supporter of equality.

The Lib Dem leader was appearing before the Women and Equalities Committee this morning, where he was challenged over the lack of diversity in his Parliamentary party. All eight current Lib Dem MPs are straight white men.

Mr Howlett, the MP for Bath, asked whether the party has had “problems” with homophobia. The MP cited instances where the Lib Dems ran against a gay candidate with the slogan ‘It’s a Straight Choice’, noting that a Lib Dem candidate in his own seat had questioned him planning to have children as a gay man.

The MP added: “I have a particular question – there are a huge number of rumours about what was going on during the gay marriage debates, particularly with yourself, when it is alleged that you went up to my colleagues, openly gay MPs, and said ‘I’ll pray for you’. How is that right?”

Mr Farron responded: “That’s a downright lie, okay? It’s a lie. This is on the record and on television, and you just repeated an untruth. That’s the reason why it’s out there… it would be good if you withdraw that.”

After Mr Howlett clarified that his remarks were allegations, Mr Farron said: “I think there are issues in terms of things that candidates say. I think they carry the party’s banner… they represent the party in various circumstances.

“The Liberal Democrats have a record of promoting LGBT+ rights that predates pretty much anybody else, and is stronger and prouder than anybody else, but that does not mean we’re immune from people choosing to behave in ways that are outrageous.

“I think I’m right in saying that in both those cases you mentioned, if individuals have been found guilty of bringing the party into disrepute, proper action should be taken.”

The leader was previously asked if he believes gay sex is a sin during a BBC interview – and refused to directly answer the question three times.

In an interview with GQ he again ducked the question, insisting: “I think that everybody is utterly equal. People should be free to love who they want and marry who they want. But I don’t go making theological pronouncements.”

Speaking to Press Association at Lib Dem conference last month, the leader was asked if he understood why his responses had caused concern.

He said: “I think it’s a peculiar one. No, is the honest answer, because I think people look at my liberalism, my desire to support people’s rights to make whatever choices they want, and I kind of also expect in the same way people… maybe it’s a naive expectation… to respect my beliefs as a Christian.

“And obviously that means a whole range of things about how I then choose to live my life. It also means that I don’t go around pointing the finger at anybody else.

“I don’t go making pronouncements on theological matters. And I think as someone who is a liberal, everybody has the right to marry who they want to marry, love who they want to love, and that’s the position we take.”

Mr Farron had previously spoken about his mixed voting record on equality legislation in a PinkNews interview, saying that he “regrets anything that gives people the wrong impression”.

The politician claimed he voted against the Programme Motion on the Marriage (Same Sex Couples) Act, because he was trying to secure more time to discuss trans issues.

He was also forced to apologise to rights campaigner Peter Tatchell – after claiming Mr Tatchell agreed with his decision to vote against 2008’s Sexual Orientation Regulations.

When challenged on his opposition, he claimed that “Peter Tatchell was on the same side as me” – but Mr Tatchell, a veteran campaigner for of LGBT rights, was actually a vocal supporter of the Act.

Making pledges on LGBT issues going forward, Mr Farron said: “On LGBT+ issues, how do you follow it? I’ll give you three things I’m very keen we do.

“One, when it comes to the equal marriage legislation, I think we really missed a trick on trans issues. On the spousal veto, I think it’s an appalling thing that one person is allowed to block another person’s freedom. We should be making that a priority.

“Secondly, it strikes me as deeply troubling is that there was no regulation of psychotherapists in the UK for quack conversion therapy.

“Thirdly, we’ve got to end the gay blood ban, which is a disgrace. My pledge to you is that my first opposition day bill will be getting rid of the gay blood ban. All of these things need to be based on the science, not on prejudice.”