There is mounting concern about the impact of government policies on women – and furious debate over the language used

Labour MPs are attempting to set up a powerful parliamentary committee to vet government policy for discriminatory effects on women, claiming that the coalition has a "blind spot" when it comes to equal opportunities.

Yvette Cooper, shadow home secretary, said the justice secretary Kenneth Clarke's controversial comments on rape this week betrayed a lack of understanding of gender issues across the government, and that there needed to be a democratic institution to act as a safeguard for women's rights. Cooper and Fiona Mactaggart, the shadow minister for women and equalities, will meet voluntary organisations to unveil the plans. The idea is attracting support from both sides of the house.

It comes amid mounting concern about the impact of government policies on women, and a furious debate over some of the language used by senior Conservatives in recent weeks, not least the prime minister's now infamous "Calm down dear" comment.

The Home Office, which includes the government equalities unit, said that the government was achieving progress for women, citing a £10m fund for rape crisis centres announced in January as an example. Theresa May, the home secretary and minister for women and equalities, is known to have been annoyed by Clarke's comments on rape this week, describing them privately as unhelpful.

Clarke's remarks came in the week that government statisticians put the number of women claiming unemployment benefits at a 15-year high, as public sector job cuts accelerate. Research published on Thursday by Coventry Universitysuggested that cuts to other benefits will cost women £30m, compared with just under £12m for men.

Cooper said that the coalition had a blind spot on women. "This is not just about revealing remarks – be it from the justice secretary or the prime minister. Women are losing out every time from government policies," she said.

"There is a toxic mix of paternalistic Toryism and laissez-faire liberalism at the heart of the government which hits women hard. Some still subscribe to the traditional Tory view of women and family life, and there is a deep and widespread hostility to state or public sector action – from tax credits to childcare – which help women get on. The result is that for the first time in generations, the clock is being turned back on women's equality."

The idea of a women and equality audit committee has already been aired in the house this year, when some coalition MPs spoke out in favour. Jo Swinson, the Liberal Democrat MP for East Dunbartonshire, said such a committee would ensure women's issues were high on the agenda. Claire Perry, the Tory MP for Devizes, said it sounded "extremely sensible". The MPs behind the plans are confident that if put it to a vote it would pass with a majority. But first they must convince the Commons authorities of the necessity for another select committee, particularly when budgets are stretched.

In a statement, May insisted the deficit was being reduced even-handedly. "Decisions to increase spending on health and child tax credits, as well introducing flexible parental leave and extending the right to request flexible working, will all benefit women. We are also taking 880,000 of the lowest-paid workers out of income tax all together, the majority of whom are women," she said. "There is absolutely nothing fair about running huge budget deficits and burdening future generations with the debts we cannot afford to pay."