Gender quotas should be mandatory for senior positions across the private and public sectors in Britain to boost the number of women in high-powered positions, according to a wide-ranging study published by the London School of Economics and Political Science (LSE).

Among its many bold recommendations, Tuesday’s report by the LSE Commission of Gender Inequality and Power suggests that “the burden of the argument should now shift from the under-representation of women to the unjustifiable over-representation of men”.

Among its key proposals, the authors of the study recommend that each political party should adopt quotas to boost the number of female MPs and ensure more balanced representation in decision-making. Parliament should pass legislation establishing a maximum limit on the proportion of MPs of either sex allowed to stand for general election, the study finds, beginning with a maximum of 70% of male candidates in each political party in the first general election following the legislation, reduced to 60% in the following election.

“This is the most controversial of our recommendations because it involves a mandatory quota on political parties in their selection of candidates for election. It is, however, increasingly the practice across Europe, including now in Ireland, and reflects frustration with the history of failed promises and insincere commitments by parties that do not yet regard the homogeneity of their representatives as a serious concern,” the report states. “Current improvements in gender balance are almost entirely due to those parties that have chosen, voluntarily, to act on this issue.” Women currently make up 29.4% of parliament.

Kate Green, the shadow equalities minister, said: “The report is right – radical action is needed to push for greater gender equality and representation.

“Labour has led the way as the only political party to have introduced all-women shortlists in addition to quotas for women standing for local government. But with the total number of women to have ever been elected to the House of Commons since 1918 remaining lower than the number of existing male MPs in the current parliament, clearly more must be done.”

Caroline Dinenage, minister for women, equalities and family justice, told the Guardian: “We now have more female MPs than ever before and a third of our cabinet is made up of women. But there is no room for complacency and we must become more representative of those we serve in order to truly govern as one nation and open up even more opportunities for people to progress, regardless of their gender or background.”

The report looked at gender inequality across four key sectors of society – the economy, politics, the legal system and the world of media, culture and communications – and found that radical change is needed in each area to speed the closing of the gender pay gap. Among the recommendations in the study, the authors called for the creation of a media watchdog on gender to monitor sexism and unequal gender representation in the media.

Evidence gathered in all four areas revealed that the structure of gender relations, especially the unequal distribution of responsibility for the care of children and of the elderly, “creates dilemmas of work-life balance which are detrimental to women’s quality of life, and to women’s life chances, across social spheres”.

While there has been some progress on the narrowing of the gender pay gap, the report notes that, compared with the EU average, the UK still has above-average gender pay and pensions gaps. The report notes there has been little improvement in the pay gap in higher-paid jobs and suggests that one reason the overall gap has narrowed is because of a decline in male earnings at the bottom.

The study found that, since the economic crisis of 2008, “the costs of austerity have fallen disproportionately on women, especially in BME [black and minority ethnic] and low-income families”. Public sector cuts to services traditionally relied on by women – childcare centres or refuges for domestic violence victims, for example – have intensified existing inequalities.