Incumbent Mayor of London Boris Johnson promised to re-enter the Greater London Authority in Stonewall’s Employer Index and defended his decision not to publish an LGBT manifesto, while Ken Livingstone quoted from the last sermon of the prophet Muhammed in a bid for cultural understanding at the charity’s mayoral hustings today.

Stonewall Chief Executive Ben Summerskill welcomed an audience to the BFI on London’s South Bank with a reference to the “media storm” that erupted this week over religious groups’ banned plans to advertise an assertion on London buses that gay people are able to turn straight and mayoral candidate’s intentions to practise a difference sort of “conversion therapy”.

The four candidates present were Conservative current mayor Boris Johnson, Labour’s Ken Livingstone, Liberal Democrat Brian Paddick and Green Party candidate Jenny Jones.

In candidates’ introductions, Mr Paddick spoke of a “very different” election to that of 2008 following the riots across London in 2011 and a desire to ensure London becomes a safer city. The only gay candidate, he also spoke of his experiences of childhood bullying due to his sexuality, the Liberal Democrats’ commitment to marriage equality and his own wedding.

Ken Livingstone spoke of his memories of the Gay Liberation Front and of witnessing campaigning in the 1980s. He elicited boos from the audience over Boris Johnson’s decision to axe City Hall Pride receptions during his tenure as mayor. Mr Livingstone also spoke of his promise to cut public transport fares by 7% and establish an energy co-op to reduce Londoners’ energy bills.

Referring to a recent and much publicised post-debate spat between the two favourites and Mr Livingstone’s emotional reaction to his own mayoral campaign broadcast, Boris Johnson said the debate should not be characterised by arguments in lifts and added that Mr Livingstone was not the only one who would “shed hot tears” if the Labour candidate returned to power.

Mr Johnson added that he would be focusing on reducing council tax and increasing police numbers, vowing to continue to support and walk London’s Pride march, though he acknowledged did not attend last year’s event, unlike Mr Livingstone.

Jenny Jones spoke of “huge cultural and ideological divides” between the candidates and a desire to set aside “macho politics”. She spoke of her party’s “progressive” stance on environmental and social issues which disproportionately affect the poor. She also pledged to drive down transport costs and called Mr Johnson’s new Routemaster-style buses an “ego project”.

Quizzed directly by an audience member on his decision to withdraw the GLA from Stonewall’s Employer Index, Mr Johnson said it had been costing the authority £2,000 a year.

Ben Summerskill assured him it was free to enter the index alongside some audience heckling over the significance of the cost. Mr Johnson, glancing at gay deputy mayor Richard Barnes, told the audience that if it were indeed free, “You’re on, we’ll do it”.

Much of the debate revolved around homophobic and transphobic hate crime in the capital, with Ben Summerskill pointing out that Boris Johnson’s 28-page manifesto on crime did not mention homophobic or transphobic incidents.

Mr Johnson, having said the rising incidence of reported hate crimes was worrying, stressed that he would continue to ensure each borough has an LGBT liaison officer, adding that the rising figure could be attributed to increased confidence in reporting of such crimes.

Mr Paddick said he would constantly tackle intolerance and continue to attend the 17-24-30 hate crime campaign’s vigils and acts of remembrance whether or not he was elected and Ms Jones described the Soho bombing as an event which shocked everyone across the city. Mr Livingstone said it was important to never “duck the issues” behind hate crime. He questioned whether Mr Johnson’s liaison officer pledge was enough.

One of the hustings’ more unusual exchanges came after a question was issued by audience member and UKIP London Assembly candidate Elizabeth Jones asking Ken Livingstone to explain the message he gave during his March visit to the Finsbury Park Mosque, now known as the North London Central Mosque.

Mr Livingstone had told the mosque he was affected by Muhammed’s last sermon’s message of equality and tolerance of others and said he would educate Londoners who had no knowledge of Islam except the words “spewed out by poisonous papers like the Daily Mail and the Daily Telegraph”.

At the hustings today, he made the point that “nothing Jesus said was homophobic” and went on to quote from the prophet Muhammed’s final sermon that “No Arab is superior to a non-Arab, no non-Arab is superior to an Arab”, that the same held between races and that men had been “created in tribes and nations”.

To audience applause, he said: “No Muslim ever came to me saying they wanted homosexuality banned.”

On supporting gay arts, Mr Livingstone said a music festival he envisaged akin to South by Southwest in Austin Texas would have a full complement of gay and transgender artists. Mr Johnson revealed London playwright William Shakespeare was “certainly bisexual”.

On city relations, Mr Paddick stressed that “nothing the mayor says should create division” and pledged to influence overseas mayors taking anti-gay stances in their cities, as Mr Livingstone said he had tried to do with the mayor of Moscow. Mr Johnson said he advocated “terse letters”.

Mr Johnson was also asked why he had not published an LGBT-specific manifesto. While saying he was “here to unite Londoners” and advocate an all-encompassing manifesto, the absence of a set of standalone pledges was drew vocal opposition from the audience.

Mr Johnson appeared to suggest in the weeks remaining before the 3 May election that he might be able to publish a document, at which point Mr Livingstone offered his for inspiration.

Asked how many civil partnership ceremonies they had each attended, Mr Paddick and Ms Jones spoke of several of their friends’ unions and Mr Paddick’s own wedding in Norway, while Mr Johnson and Mr Livingstone admitted they were not often invited to weddings and ceremonies outside City Hall.

Ben Summerskill, Stonewall’s Chief Executive said following the hustings: “It’s really impressive that all of the main mayoral candidates wanted to engage lesbian, gay and bisexual Londoners – something that would have been unthinkable 15 or 20 years ago. What was particularly interesting was that many of the people in the audience were completely undecided about how they were going to vote, so clearly no-one should take London’s 350,000 gay voters for granted.”