London mayor Ken Livingstone can justifiably boast that he has done much over the last 30 years to support lesbian, gay, bisexual and transgender (LGBT) Londoners. As leader of the Greater London council in the 1980s, he was the first major politician to speak out publicly in support of gay human rights. His funding of previously unsupported LGBT welfare and advice agencies was trailblazing and immensely positive.

In his first term as mayor of London, Livingstone set up the UK's first same-sex partnership register, which paved the way for the subsequent legislation of civil partnerships. But during his second term as mayor, he caused widespread dismay in the LGBT community when he welcomed to City Hall as his "honoured guest" Yusuf al-Qaradawi. The mayor subsequently repeatedly excused and defended the viciously homophobic and murder-inciting cleric.

Qaradawi supports the execution of gay people in Islamic states, the killing of Muslims who abandon their faith, wife-beating, female genital mutilation, forcing women to wear the hijab, terrorist attacks on innocent civilians in Israel and the flogging of women who have sex outside of marriage. He also said the 2004 Asian tsunami was punishment by God because the people who died had allowed their countries to become centres of "sexual perversion".

Together with many other people, I criticised Livingstone over his embrace of Qaradawi. He responded with the wholly untrue claim that I am an "Islamophobe" and a person with "a long history of Islamophobia".

Since then, despite an occasional pro-gay initiative, like opposing Westminster council's attempt to ban rainbow flags in Soho, Livingstone's record of supporting the LGBT community has been somewhat patchy.

LGBT Londoners are, of course, not only interested in LGBT policies. Like the rest of London, they are also concerned about transport, crime, housing and the environment, as well as the candidates' stance on matters that specifically affect lesbian and gay people.

On four issues Livingstone needs to explain why he has let down the LGBT community. The other mayoral candidates also need to state where they stand. What are the Conservative, Lib Dem and Green policies on these questions?

Refusal to fund the gay football world championships in London

Livingstone has refused to contribute to the funding of the 2008 international gay and lesbian football association world championship, which is being held in London in August. London has won the honour of being the host city, and the UK's Stonewall FC team is a strong contender for the world title, but the mayor is withholding financial backing.

Livingstone also refused to sign a letter of support for the associations's grant application to the lottery fund. Having the high-profile support of the mayor would increase the likelihood of the grant succeeding. It costs nothing to sign a letter of support.

The unexpected lack of financial assistance from the mayor has contributed to the association being left with a funding shortfall. How does the mayor justify this denial of a few thousand pounds to the gay football world championships when he has showered billions on the 2012 Olympics? Where do the other mayoral candidates stand on funding the gay football world cup and similar gay sporting events? And will they offer financial support to increase youth, women's, disabled and ethnic minority participation in sport?

Lesbian and gay museum

During the 2004 Mayoral election campaign, Livingstone promised to fund a lesbian and gay museum, which is now called Proud Heritage. The idea is to add to the diversity of London's museums by creating a new institution dedicated to documenting and celebrating the lives and contributions of LGBT people, in a similar way to the existing specialist Jewish, children's and slavery museums.

It took until 2007 for Livingstone to grant a rather modest start-up grant of £5,000. Further money was pledged. Proud Heritage made a bid for an additional £10,000, so it could launch the first stage online version of the museum this week. The mayor eventually agreed a further £5,000. This money has been contracted by Livingstone but not delivered as of 15 April. Why not?

On the basis of Livingstone's contracted £5,000 grant, Proud Heritage organised development work. This work on the website, which opens on April 18, has not been completed because Livingstone's money has not materialised. This has created needless last-minute stress for the Proud Heritage organisers.

Why has Livingstone delayed his election pledge on the lesbian and gay museum? Why, four years after his promise, has the Proud Heritage project been underfunded by the mayor? What will other candidates pledge towards this project?

Proud Heritage is, so far, only an online museum. Will the mayoral candidates support and help finance a physical LGBT museum as well?

Mayor's LGBT forum

The mayor's LGBT forum was set up to liaise with the LGBT community. But from the outset it has been structured in a wholly undemocratic way.

Why isn't the forum allowed to elect its own chair? Why did Livingstone impose as chair one of his own people, a straight woman, Anni Marjoram? Why is the LGBT forum banned from proposing resolutions or holding votes on policy recommendations to the mayor?

Attempts to propose and vote on policy issues are ruled out of order by the chair. This has disillusioned many of us who proposed and backed the forum as an open, democratic space for dialogue and consultation.

The forum is now widely dismissed as a PR exercise, with no real power or influence. Many grassroots activists no longer bother to attend. What is the point? Anything that questions mayoral policy doesn't get on the agenda and uncomfortable debates are curtailed by the chair.

How does the mayor explain the fact that many grassroots LGBT campaigners in London no longer participate in the forum? What does he say to allegations that it has become an unrepresentative forum attended mostly by pro-Livingstone factions and LGBT groups hoping to get money out of the Greater London authority? What would other mayoral candidates do to rectify this democratic deficit?

Underfunding of LGBT groups and events

The mayor has given millions to black projects, which is a very good thing. The empowerment of ethnic communities is vital to redress social exclusion and discrimination. But Livingstone has granted comparatively little to LGBT projects. The mayor keeps promising LGBT funding but he seems rarely to deliver. He is quite good at verbal support, but little more.

How does Livingstone justify the millions of pounds he and the London development agency have given to black community groups and the largesse provided for the St Patrick's Day events, compared to the much smaller grants that he has given to Pride London and LGBT community organisations?

In 2006, the mayor gave £175,000 to the St Patrick's Day festival and £288,000 to the Rise festival - but only £100,000 for the LGBT Pride London festival.

I don't begrudge support for Irish, Black, Hindu, Jewish, Sikh, Muslim and women's groups and events. The mayor has duty to support all of London's wonderful diverse communities. He is right to do so. It helps create a more liberal, tolerant and cohesive city.

But shouldn't there be a more equitable distribution of mayoral funding, with all community events receiving roughly similar levels of financial backing? Or at least there should not be such huge disparities in the mayor's financial support. Where do the other candidates stand on this question?

Livingstone's mishandling of these four issues has implications way beyond the LGBT community. It is symptomatic of a style of governance that adversely impacts on many Londoners. As well as Livingstone, all the mayoral candidates need to address this issue, so Londoners know what they will do if they are elected mayor on May 1.