Lynne Featherstone, the Liberal Democrat equalities minister, has attacked the "hideous" ideas of David Cameron's closest aides in a sign of coalition tensions over the government's family policies.

In a wide-ranging interview with the Observer, Featherstone said it was vital the coalition delivered on its family-friendly rhetoric, amid concerns that the government is haemorrhaging support among disillusioned female voters.

In a forthright attack on some of the advisers shaping government policy, she criticised the role of Adrian Beecroft, a venture capitalist tasked with reporting to the prime minister on how to cut regulation on business. Beecroft is understood to have recommended a U-turn on government policies on shared parental leave and flexible working.

The proposals, outlined in a white paper, would allow couples greater freedom to co-ordinate maternity and paternity leave. A separate proposal would make it easier to request flexible working hours.

Featherstone told the Observer that Beecroft's recommendation that the moves should be shelved was not acceptable and would be "swept away". She also made her feelings clear over a recent "blue sky" proposal from Steve Hilton, the prime minister's director of strategy, suggesting that the government could scrap maternity pay altogether. Featherstone said: "Well, I might talk about scrapping Steve Hilton."

Such language is a sign of growing concern within the government that it is looking out of touch with female voters and that those close to Cameron are not getting to grips with the problem.

Beecroft was brought into Downing Street over the summer to offer ideas to Cameron on laying the groundwork for economic growth He is understood to have proposed a series of measures to lift regulation, which a number of Conservative ministers are minded to support.

But Featherstone, MP for the north London constituency of Hornsey and Wood Green, said: "Whatever is in this Beecroft report, I think, will be swiftly swept away. These are hideous suggestions … What I would say about them is that it would be absolutely extraordinary if we were to abandon our commitment to those flagship policies.

"It is absolutely vital that we deliver on our rhetoric around family-friendly issues. I wouldn't support that, Nick [Clegg] wouldn't support that, and quite frankly David Cameron was campaigning last year on being the most family-friendly government. I would be very surprised if he supported that."

There are worrying signs that the government's policies are hitting women disproportionately, while measures to encourage equality in business are simply being ignored. Last week the number of unemployed women hit 1.06 million.

Meanwhile, the prime minister felt forced to write to the country's major companies last week after a disappointing response to the government's drive to put more women on boards. Just 33 companies in the FTSE 100 have announced that they will aim for a minimum of one in four female board members by 2015 – a voluntary target imposed by the Davies review in February.

And there is a concern, in particular among the Liberal Democrats at the highest level of the government, that Cameron may be listening too closely to advisers who believe that regulation protecting and promoting women in the workplace is an obstacle to growth.

Featherstone said: "In a coalition government there are eddies, currents and flows and tides all over the place, and it is no surprise to me that there is a wing of governmental advice that says that not a wind should blow on business.

"And it will be no surprise that the pushback will be that actually a bit of fresh air would do a lot of good and the bottom line is that [encouraging more women in the work place] improves the bottom line."

In a development likely to further infuriate the right wing of the Conservative party, she added that the government could in fact usher in more regulation in the form of the enforcement of quotas on directors. "My view on that is I would never like to say never, because I think any negotiation should always have an ultimate consequence," she said.

Featherstone's brief also includes tackling violence and bigotry towards women and the lesbian, gay and transgender communities, and she said it was "a good thing" that the government is looking to use aid to guide countries away from homophobia.

However, she risks the wrath of this country's taxi drivers by admitting she generally avoids speaking to them. "I remember going in a taxi somewhere, and the taxi driver was talking, I don't remember why we were talking about it, I certainly didn't bring it up. I try not to talk to taxi drivers. Ever since I was chair of transport in London at the London assembly and in charge of taxis. And, you know, he was saying some really foul things and obviously I then leapt to the defence of it."