Amy Zala has arguably the best prop of Leicester University’s freshers’ week. Carrying a 1.5m inflatable penis, the 19-year-old sociology student, who is part of the university’s sex education society Sexpression, dances around the freshers’ fair and explains why she’s so excited.

“I am just so happy that HeforShe is coming here,” she says, in between trying to get new recruits. “There is so much sexism and lad culture at university, so just hearing people talk about these things makes me really proud.”

HeforShe, a UN campaign fronted by the actor Emma Watson that encourages men to speak up and take action on gender equality, is about to embark on a tour of 10 universities. It kicks off at Leicester, before heading to Paris’ Sciences Po, the London School of Economics and Nottingham, among others.

Even the rugby club are on board. “I had my picture taken for it, we’ve been asked to get involved and we are,” says club captain Harry Tillyer, 20. “We sometimes get a bad rep, but the whole thing is quite cliched. I’m not saying there is no sexism sometimes but we are really trying to get over that.”

The club has got a social media policy, and a disciplinary procedure to tackle bad behaviour now, he adds.

Asked if the team see themselves as feminists, club hooker Adam King, 21, chips in: “I’m all for equality. To be fair it’s never been a outwardly sexist club, but maybe in the past when people have had a drink they say things they wouldn’t dream of saying when they were sober.”

Bringing men into the heart of tackling gender inequality has not been without controversy. Some in the women’s movement feared men would dominate debate, others scoffed at the idea of needing to be “rescued”.

But for feminist students at Leicester, trying to recruit the other half of the world’s population for the fight against gender equality makes a lot of sense. “I think a lot of men hear the word feminism and think that it’s about putting men down to raise women up, but really it’s about the elevation of both sexes,” says Tyler John, a feminist and proud.

“If you are a male feminist, people are like – do you hate men? There’s such a lad culture that being at all feminine is seen as weak or whatever. But this isn’t 1950, it’s the 21st century.”

At the event Leicester University’s vice-chancellor Paul Boyle rattles through some of the gender imbalances that persist. Only 17% of FTSE 100 companies are headed by women, while only 8% of surgical consultants, 20% of professors and 14% of university vice-chancellors are women, saying these inequalities are “restricting the opportunities of some and denying society the benefit of talented people”.

The campus saw a lecture hall filled with keen faces – about half of them male – to hear HeforShe’s director Elizabeth Nyamayaro speak. She acknowledges that when the campaign, which has garnered the support of men from Matt Damon to Desmond Tutu, launched a year ago there was a lot of “trepidation and hesitation” about involving men in a battle traditionally owned by women.

“This is not about men saving women, or seeing women as helpless,” she says. “We want to dismantle the patriarchy, but how can you achieve equality if you don’t engage with the men who are very often holding positions of power? It’s about solidarity, mobilising all of society.”

472,000 men have signed up since the campaign’s launch, while 10 business leaders including Unilever and Vodafone have committed to taking action. The campaign also hopes to sign up 10 heads of state – the leaders of Japan, Indonesia and, of course, Sweden and Iceland are among them – but two places remain to be filled.

Asked if the UK prime minister was invited to take a role, Nyamayaro says the invitation went to all world leaders. So could David Cameron still sign up? “He has an open invitation,” she says.

Speaking at the event, education secretary Nicky Morgan, who also holds the government’s equality brief, told students that gender equality is one of her greatest passions and was a motivating factor for her going into politics.

Asked afterwards if the government was doing enough to tackle deep-seated inequalities, including the representation of women in parliament which now stands at 29%, she said: “We all have a job of work to do, men and women, in my case it’s going out to women and explaining why being a member of parliament is such a great job.”

In David Cameron, she says “you could not have more of a champion of equality”. But asked if the prime minster – who has seven women in his 22-member cabinet – should, therefore become a state ambassador for the campaign, she ducks the question. “The prime minister is already championing everything we have talked about today,” she says.