Harriet Harman, the acting Labour leader, today called for a rule change to ensure half the party's shadow cabinet are women.

In a speech to the Unite union's annual conference in Manchester, Harman said it was "time for Labour women to step out of the shadows".

She said there were now 81 female Labour MPs, more than those in all the other parties put together.

"Labour is the only party in parliament which speaks up for women in this country," she added.

"We have some excellent experienced women and some brilliant new women MPs. We still do have twice as many men MPs as women. The Labour men are great – but they are not twice as good as the women."

Harman's call was backed by Ed Miliband, the shadow climate change secretary. In a tweet sent today, Miliband said: "Very sympathetic to what Harriet has said today on 50% women in shadow cabinet. Will ultimately be a PLP decision, but I will be supporting it ."

Harman has ruled herself out of the Labour leadership race, to the surprise of many observers. Last month, she said she could not run for the position of Labour leader while holding the post of deputy.

Yvette Cooper, the shadow work and pensions secretary, has also ruled herself out of contention. Her husband, Ed Balls, will contest the leadership. Cooper berated David Cameron in the Guardian last week for "shocking sexism" in joking that Balls had ordered her not to stand.

Diane Abbott, the MP for Hackney North and Stoke Newington, in London, has thrown her hat into the ring, but has yet to secure the 33 nominations from parliamentary colleagues she needs to formally enter the race.

Jon Trickett, the MP for Hemsworth who served as Brown's former private parliamentary secretary for the last 18 months of his premiership, gave his nomination to Abbott todayyesterday.

The leftwing MP, whose constituency neighbours those of Ed Miliband and Balls, said that now both were in the race he had decided to back Abbot to ensure her voice was added to the leadership debate.

"I listened to the views of Labour members and trade unions, and they want to see the widest possible debate," he added.

Harman used some of her six questions to Cameron at yesterday's prime minister's question time to take him to task over the decision to grant anonymity to men accused of rape, and over tax breaks to married couples.

She said Labour would be an "effective" opposition, speaking up for public services and jobs, and warned that the party's opponents would make a determined effort to denigrate everything it had done in government.

"We will not let them," she said. "For every child who, instead of being cooped up in a flat, is playing in a brand-new children's centre, that is our legacy.

"For every patient who, instead of waiting in pain, is cared for by doctors and nurses in a brand-new hospital, that is our legacy. For every villager in Africa whose life has been transformed by cancelling third-world debt, that is our legacy."

The acting leader gave her address to the union conference on the same day her husband, Jack Dromey, gave his farewell speech as Unite's deputy general secretary following his election as MP for Birmingham Erdington.

Harman said rebuilding and renewing Labour following the election defeat was an important task, stressing that the party had to "listen and learn".

The Labour leadership election will involve up to 4 million people, making it the biggest election in any political party or any organisation in this country, she said, adding: "This leadership election is crucial opportunity for the Labour party to reflect, renew itself, and re-engage with the people of Britain."