A gender imbalance across local government has been exposed in a damning report that suggests councils – especially the new mayoral authorities – are lagging behind even Westminster in taking steps to improve equality.

The study, published on Sunday by the Institute for Public Policy Research, reveals that only 33% of councillors and 17% of council leaders in England are women, something the thinktank suggests is causing a “democratic deficit”.

In the new mayoral combined authority boards, only 4% of constituent members – those with full voting rights – are women and all six bodies are led by men. The West Midlands, Cambridgeshire and Peterborough, the Liverpool City Region and the West of England authorities are all without any female constituent members.

The IPPR calculates that, to achieve equal numbers of male and female councillors in England, 3,028 more women need to be elected, an increase of more than 50% on the 5,800 or so currently in power. The thinktank estimates that, to achieve parity in gender balance, more than 12,000 women would have to apply for elected positions on councils. The shortfall means many policies that have a direct impact on women’s lives are being drafted at the local level by male councillors with little practical experience of the issues at stake.

The report, Power to the people? Tackling the gender imbalance in local government & combined authorities, finds that women face a number of barriers to entering local government and progressing into leadership roles.

Despite calls from politicians on all sides for more women to enter politics, the percentage of female candidates selected by parties to stand in council ward elections has flatlined, at around a third, since 2007. By contrast, there have been much faster gains in parliament – the number of female MPs elected rose by 9% in the 2017 general election compared with 2015. In the past 20 years, the proportion of women councillors has grown by 5%, but at this rate it will take another 68 years to reach equal representation.

Facebook Twitter Pinterest Jess Phillips MP: ‘Without a target or a quota, nothing is going to change.’ Photograph: Fabio De Paola/REX/Shutterstock

Labour MP Jess Phillips said it was time to consider a change to the law. “Councils and public bodies in the future need to look at whether they want to have targets that lead to local action. Without a target or a quota, nothing is going to change.”

Despite a new generation of young women participating in politics, with voter turnout among women aged 18 to 24 reaching 53% at the last election compared with just 44% in 2015, the report finds that political parties are failing to engage more women, with the result that they are less likely to go on to become local councillors.

Women make up only 38% of Labour party members and only 36% of Conservative party members.

“It cannot be right in 2017 that there are barely any women represented in the leadership of our newest democratic institutions, the combined authorities,” said Clare McNeil, IPPR associate director. “Efforts made to address this in Greater Manchester and elsewhere are to be welcomed, but radical change is needed if devolution is to be about bringing power to the people, rather than consolidating it among white middle-aged men.”

The report states: “Many local government policy areas have a much greater impact on women than on men. For example, local government has oversight of childcare provision as well as responsibility for delivering and funding social care. Women, who in 2017 still shoulder the greatest burden of caring responsibilities in the family, are simply more affected by decisions on who gets state-funded care, and how it is delivered.”

The IPPR wants leaders of political parties to commit to achieving a 50:50 balance in male-female party membership. And it wants authorities to make a commitment that at least 45% of those on combined authority boards are women. If significant progress towards greater gender balance in local government and combined authorities cannot be achieved through these changes, then it says legislation should be introduced requiring elected positions to be filled equally by genders, or with a split of 60:40 or better.

“Political institutions and parties must introduce more ambitious quotas to improve representation in the short term,” McNeil said. “And local government should do more to encourage women to stand and support them effectively once they have been selected. Without these measures representation will continue to be deeply unequal. Leaders of political parties should back our call to recruit the 12,000 women needed to stand for election to achieve a better gender balance in local government by 2025. This would be a fitting way to mark next year’s anniversary of 100 years since the first women got the vote.”

Marianne Overton, vice-chair of the Local Government Association, believes that “change will only come about through a mix of support programmes and direct action from political parties to encourage and sustain aspiring female councillors”.