Political parties should be forced to publish a gender breakdown of their candidates for parliament to help get more women into senior roles, campaigners said on Sunday.

The Electoral Reform Society and the Fawcett Society are among those calling on the government to enact legislation obliging parties to reveal what proportion of their candidates are women – and how many of those go on to win.

Campaigners believe the publicity that would come with regular reporting of the “gender gap” in politics would help to put pressure on parties and encourage more women to stand for office.

Currently 32% of MPs and 33% of local councillors in the UK are women.

Section 106 of the Equality Act 2010, passed by the last Labour government, made provision for political parties to publish the information but it has never been enacted.

The campaigners would like to see Section 106 enforced and extended to cover local government too.

Britain’s biggest companies have been scrambling to explain their gender pay gaps after new rules obliged them to publish the information, and equality campaigners believe the public availability of data encourages progress.

Monday is the 90th anniversary of the 1928 Equal Franchise Act – which gave women the same voting rights as men – and marks the beginning of a government-backed National Democracy Week.

Jess Garland, director of policy and research at the Electoral Reform Society said: “Now that companies have revealed their gender pay gaps, it’s time UK parties tackled the inequality in their own back yards. We’ve seen businesses play their part – now government and political parties must play theirs in showing their diversity figures.

“Much like the gender pay gap, political inequality is holding back progress in this country.”

The demand is also backed by Helen Pankhurst, women’s rights activist and granddaughter of the suffragette Sylvia Pankhurst, and other members of the Centenary Action Group, which is urging greater female participation in politics, 100 years after women were given the vote.

MPs on the women and equalities select committee also called for Section 106 to be enacted, in a report published last year aimed at redressing gender balance in parliament.

“Publication of this information is vital for public and parliamentary scrutiny of the record of political parties in selecting a diverse slate of parliamentary candidates,” the committee said at the time.

The legislation also covered the publication of information about other “protected characteristics” including sexual orientation and race.

Labour will hold a debate in parliament this week to mark the 90th anniversary of the Equal Franchise Act.

The shadow equalities minister, Dawn Butler, said: “This anniversary is a reminder of the importance of addressing the inequalities faced by all women – working class women, women from ethnic and religious minorities, disabled women and LGBT+ women, leaving no one behind.”

Theresa May unveiled a new statue of the suffragist Millicent Fawcett in parliament square earlier this year – the first of a woman in the prominent Westminster spot.

A spokesperson for the Government Equalities Office said: “Transparency is important to the Government Equalities Office, as our gender pay gap regulations have shown, and we are keen to see where else this approach could help shine a light on areas where women and other groups are held back.

“This parliament is the most gender and LGBT diverse ever, but there is still more to do.”