New laws should be considered to stop non-disclosure agreements being used to silence the victims of sexual harassment and punish those who abuse their power, a former Conservative cabinet minister has said.

Nicky Morgan, the former education secretary and women’s minister, said the time had come to ask if new powers were needed to tackle harassment as part of Theresa May’s pledge to tackle the “burning injustices” in Britain.

It follows a series of scandals that have hit Hollywood, Westminster and other institutions. Film mogul Harvey Weinstein was toppled by a string of allegations, while two cabinet ministers also lost their jobs over inappropriate behaviour. Other MPs are still facing allegations.

Meanwhile, the Nobel prize for literature has been postponed this year in the wake of sexual assault allegations connected to the Swedish Academy, which awards the prize.

Writing as part of a new cross-party essay collection on injustice, published by the Joseph Rowntree Foundation charity and the Bright Blue thinktank, Morgan said women in Britain still face “unjustifiable barriers”.

“The Office for National Statistics Crime Survey for 2016-17 showed that one in five women in the UK has experienced some kind of sexual assault,” she writes. “In England and Wales, in 2015-16, there were 4,094 sex discrimination cases taken to an employment tribunal.

“And, horrifically, in spite of a long list of criminal offences outlawing domestic violence, two women a week are killed by their current or former partners in England and Wales.

“Laws have been passed to clamp down on sexual harassment, abuse and stalking, yet projects such as ‘Everyday Sexism’ record the deliberate and casual misogyny which girls and women still have to put up with. In many cases, harassment happens because powerful men take advantage of their status to harass women they work with. Is it time for an ‘abuse of power’ offence? Could whistleblowing protections be extended to those who call out harassment? Should non-disclosure agreements in such situations be outlawed?”

A series of allegations made against MPs has seen Westminster caught up in the issue. Charlie Elphicke, the Tory MP for Dover and Deal, was suspended from the Conservative party in November and was interviewed under caution by police in March after allegations of sex offences. He denies the claims.

Michael Fallon resigned as defence secretary last November after admitting his past behaviour had “fallen short”. Damian Green lost his job as first secretary after admitting he lied about the fact that pornogrpahic images were found on his Commons computer.

Meanwhile, the speaker John Bercow is facing allegations that he bullied members of his staff – an allegation he denies.

In her essay, Morgan calls on her party to champion equality and warns it against being “suspicious of calls for equality of outcome”.

“Even now, this Conservative government is proposing that the EU Charter of Fundamental Rights, which includes sections on equality and prohibiting all forms of discrimination, does not need to continue to be an explicit part of UK law after Brexit,” she writes.

“Gender discrimination starts early. So, there must be a more explicit focus on it within the education system. In the same way that we need more male primary school teachers, we need more female head teachers: more flexible working patterns in our schools and colleges is essential.”

She also calls for more rights for women going through the menopause. “Many health conditions faced by women now, happily, attract fierce attention and widespread support. Breast cancer, for example, receives significant levels of funding.

“But there are still issues – for example, early screening for ovarian cancer or tackling the taboos around the menopause – which need greater focus. Every woman goes through the menopause, but are affected differently, some very negatively. Women should not have to face inconsistent support from employers during what can be a very difficult time.”