London's mayoral candidates have canvassed for the gay vote a day after the incumbent, Boris Johnson, intervened to block the capital's buses from carrying adverts from a Christian group that claimed therapy can 'cure' homosexuality.

Johnson was joined by his four main challengers – Jenny Jones (Green), Ken Livingstone (Labour) and Brian Paddick (Liberal Democrat) – at the event, hosted by Stonewall. All wore T-shirts featuring the gay rights group's campaign slogan 'Some people are gay. Get over it'.

The advert blocked by Johnson after a storm of protest on Twitter was due to say: "Not gay! Post-gay, ex-gay and proud. Get over it!"

Johnson was criticised at the hustings for refusing to co-operate with Stonewall in its survey of London employers and their treatment of gay staff. But the mayor said he would be happy to allow the Greater London Authority to be considered for Stonewall's list of London's top 100 employers as long as there was no fee.

Johnson responded to further criticism by promising to address remarks in his manifesto specifically at the needs of the gay community. Livingstone said the Tory mayor could borrow the section in his own manifesto that is directed at the gay community. Livingstone has pledged to appoint a lesbian, gay, bisexual and transgender advisor if he is elected mayor.

The Labour candidate and former mayor was asked to explain his remarks about wanting London to be a "beacon" for the philosophy of the Prophet Muhammad. Livingstone explained that there was nothing in the sermons of Muhammad that could be construed as a justification for discrimination.

Livingstone told the crowd at the South Bank Centre that Muslims were now the target of prejudice which had previously been reserved for the gay community. "In 1906 the front page of the Daily Mail's headline was 'Jews bring crime and disease to Britain'.

"Then it was the blacks, then it was the Irish, then it was the lesbians and gays – there has always got to be an enemy. Rightwing politicians pander to bigotry."

Paddick, the Lib Dem candidate and former deputy commissioner of the Metropolitan police, said there needed to be a "culture of change" at Scotland Yard to eradicate prejudice.

He said: "A poll the other week showed that 20% of Londoners do not believe that the police are on their side and I think that proportion may even be higher because of the history that the LGBT [lesbian, gay, bisexual and transgender] community has had, particularly with laws which specifically discriminated against men and the enthusiasm with which the police enforced those laws.

"What I promise you is if I become the mayor and the crime commissioner on 3 May, I will put that pressure on to deal with racism and homophobia within the police."

On Friday, Johnson ordered his transport chiefs to pull the adverts booked by two conservative Anglican groups following outrage among gay campaigners and politicians saying that they were homophobic. The adverts, pulled just days before the posters were due to appear on buses in the capital, were booked on behalf of the Core Issues Trust whose leader, Mike Davidson, believes "homoerotic behaviour is sinful".