Who cares about violence against women? Not just rape and sexual assault, which are big issues for all women, but the additional hazards, such as forced marriage, that face women from ethnic minorities. How far politicians will go in confronting these subjects is being put to the test – during the hotly contested election for London's next mayor.

There have been many horrific "honour" killings in the city. In 2006, Banaz Mahmod, a 20-year-old Kurdish woman from south London, was murdered on the orders of her father and uncle. Banaz was raped, strangled, stuffed into a suitcase and buried. She had repeatedly told police that her life was at risk.

In November, a women's organisation, Imkaan, looked at the extent of "harmful practices". The Government's Forced Marriage Unit dealt with 330 cases in London in 2010, and scores of women contact specialist services every week. Imkaan found that around 7,000 women who have suffered female genital mutilation give birth in London each year, and their daughters are at risk of FGM too.

Imkaan's director, Marai Larasi, called for protective measures and argued that the issue was "neglected because of fears... of being labelled at best culturally insensitive and at worst racist". It's a belief echoed by other professionals working with victims from ethnic minorities, who say the problem is made worse by male community "leaders" defending patriarchal practices.

Ten days ago, the four main candidates in the London mayoral election were invited to a hustings staged by End Violence Against Women. EVAW has produced a 10-point plan designed to make London "the world's safest city for women". No candidate turned up, not even Labour's Ken Livingstone, who issued a manifesto specifically aimed at women last week. Each sent a representative, but it wasn't a convincing display of commitment to the subject.

I don't like Boris Johnson, but the Mayor's office helped fund the Imkaan report and he's promised to establish a task force "to confront female genital mutilation and other harmful cultural practices". The Greens' Jenny Jones has promised a London-wide review to ensure that such practices are stopped.

Labour's manifesto is strong on tackling rape and sexual harassment; the Lib Dems' has a useful section on sexual violence. Neither mentions forms of violence specific to women from ethnic minority communities. When I pointed this out on Friday, Brian Paddick's spokesman said the candidate would sign EVAW's plan, and work with the police and black and ethnic minority communities to "eradicate these abhorrent practices".

Livingstone's spokeswoman told me he had "very strong views" on the subject and cited his support for criminalising FGM as leader of the GLC, 30 years ago. A couple of hours later came the news that Livingstone and his deputy, Val Shawcross, had signed EVAW's plan and would enact its policies if elected.

Women are half the population and we care about violence against black and ethnic-minority women. If they want our votes, politicians had better take note.