David Cameron has done an extraordinary thing. He apologised last week for the homophobia of his own party, singling out Section 28, the Thatcher government's infamous ban on the "promotion" of homosexuality by local authorities.

Condemning it as a "mistake" and "offensive", he pledged to make the Tories the party of gay equality: "The Labour government has made some important changes. I think we have further to go," he told the Pink Paper.

These crucial words are Cameron's bold, praiseworthy commitment to further policy changes to remove the remaining vestiges of homophobia. My challenge to David Cameron is this: what specific additional legal reforms will you pledge to the lesbian, gay, bisexual and transgender (LGBT) community? What would you do as prime minister to end the homophobic discrimination that Gordon Brown is refusing to abolish?

Take homophobic violence and hate crime. Successive Labour home secretaries have given visas and work permits to Jamaican reggae singers such as Bounty Killer who incite the murder of LGBT people.

Inciting murder is a serious criminal offence, yet these singers are allowed to come to Britain, while the leader of the US Nation of Islam, Louis Farrakhan, has been banned from Britain for two decades. I may disagree with Farrakhan's views, but he has never incited violence against anyone. Why the double standards?

Moreover, the Government, police and Crown Prosecution Service permit record stores and radio stations to promote songs that encourage the killing of LGBTs. Neither Labour nor Tory ministers would tolerate similar "murder music" against Jewish or black people. Why aren't LGBTs receiving the same legal protection against incitements to kill them?

Gordon's government is refusing asylum to LGBT refugees who have been jailed and tortured in countries such as Saudi Arabia, Iraq, Nigeria, Jamaica, Iran and Uganda. The Home Office says they won't be at risk if they go back home and stop having gay relationships. It never makes such onerous demands on political, religious or ethnic refugees.

Labour said its Equality Bill would harmonise the patchwork of equality legislation. It won't. Harassment based on sexual orientation is explicitly exempted. This exemption applies to schools. They will have no legal obligation to prevent the harassment of LGBT pupils, despite the pandemic of homophobic bullying. Meanwhile faith schools will be allowed to promote their own religious ethos, which may include anti-gay teachings.

The Government supports the National Blood Service policy of banning all gay and bisexual blood donors for life, regardless of their sexual behaviour and HIV status. This is a bigoted ban. Most gay and bisexual men do not and never will have HIV. Those who have only safe sex and who test HIV negative can give blood safely. Banning them is contributing to the shortfall in blood donations.

Gordon Brown defends the prohibition of same-sex marriage. Instead of repealing this discrimination, Labour's civil partnerships reinforce and extend it. They are for same-sex couples only. Conversely, marriage remains reserved for heterosexuals. In addition, gay-supportive churches that want to conduct civil partnerships are prohibited by law from doing so. Welcome to segregation, Labour-style.

Gordon Brown could have ended all homophobic discrimination, but didn't. By leading on further gay law reform, the Tories can outmanoeuvre Labour and win lots of LGBT votes. David, are you up for it?