The women who gathered in London on Saturday to mark the centenary of a mass rally staged by 50,000 suffragettes in Hyde Park posed a clear question: how far have British women come since that summer's day in 1913? In answer it is possible to point to Margaret Thatcher, or Dame Stella Rimington, the first woman to run a security service, or Karren Brady, vice-chairman of West Ham football club, and to conclude that the sky is the limit. We can indeed point beyond the sky, to astronaut Helen Sharman; not just the first British woman in space but the first Briton in space.

Sharman's case might seem to prove that female role models are not always household names and are frequently people driven purely by personal ambition, rather than by crusading zeal. Yet in a century of feminist campaigning it is those women who have publicly challenged gender stereotypes that have made it possible for others to soar to the top.

As a groundswell of new feminism dubbed the fourth wave begins to have true influence, a small group of individual activists have emerged who stand comparison with a dogged suffragette like Emmeline Pankhurst, or with Millicent Fawcett, the social pioneer who addressed that rally in July 1913. But by targeting key cultural institutions and communicating directly via the internet they are setting a new feminist agenda.

Last week Mark Carney, the new governor of the Bank of England, speedily had to produce a banknote from his back pocket to placate Caroline Criado-Perez. She had argued, along with 35,000 supporters, that British currency should celebrate the achievements of women as well as men. Plans to replace prison campaigner Elizabeth Fry on the £5 note with a design featuring Winston Churchill outraged her and she decided, in the face of many other potential feminist causes, to take up arms. As a result the next £10 note will bear the face of Jane Austen. "People have said this was not such a big thing to tackle, but I didn't especially pick on banknotes," Criado-Perez, 29, said. "I just saw the new note and thought, 'I am not having this'. And the Bank of England is not a small institution."

Charging the barricades alongside Criado-Perez are Laura Bates, founder of the international website Everyday Sexism, Kat Banyard of UK Feminista, who campaigns against lads' mags, Lucy-Anne Holmes, who is calling for an end to topless page three models, and the irrepressible Amanda Fucking Palmer, the US performer who hit back at the Daily Mail this month after it drew attention to the fact her breast was revealed at her Glastonbury set.

Palmer hit back, writing an open letter to the newspaper in 3/4 time and performing it nude on stage at London's Roundhouse. A recording has gone viral on YouTube. She told the Observer: "Seeing the media cross-fire after the song went up on YouTube was fascinating, it was like I'd created an inadvertent rallying cry against the Daily Mail. Tabloid culture and their 'she's-too-fat-she's-too-thin' commentary is something I think we just get used to and stop noticing, like basic air or noise pollution.

"The worst part of it is how it cements the fear that young girls are already battling, that the world is just waiting to judge you, your clothes, your weight, your looks. It baffles me that the vast majority of comments on some of my YouTube videos that have over a million hits are about the existence of my armpit hair, not the music, not the actual artistic content. And it's 2013. I thought this was supposed to be the future. What happened?"

Criado-Perez, who studied English at Oxford and now lives in London, has been uplifted by the recent mood. "It is really exciting the way it has all come together for women. I can't help feeling emotional, but you can't put it down to one thing. For a start, the internet has been important as a way to fight back against the homogeneous message that women were all happy and equal now. It has given a voice to those who want to say that we are not." While the internet has helped Criado-Perez spread her message, it is also the medium by which she was subjected to a stream of abuse, including rape threats, following her victory. She has vowed to fight back, saying: "Someone issuing rape threats wants women to shut up, to get off Twitter and not appear on the news. We can't let them win."

Her Bank of England win has been slightly dented by the odd choice of Austen quote on the new note: "I declare after all there is no enjoyment like reading." From Pride and Prejudice, it is a phoney line delivered by Caroline Bingley, a character on the make, rather than a genuine book lover. "I am a bit disappointed," said Criado-Perez. "It looks like they have quickly searched for an Austen phrase and it illustrates my suspicion they chose Austen because they don't get her. They think she is safe and nice. It would be great if they replaced it now with her line about women being written out of history."

Holmes, who campaigns against page three, has not yet tasted complete victory, but last week David Cameron faced tricky questions on BBC Radio 4's Woman's Hour and one of the Sun's key advertisers, Lego, announced it would stop running promotions, although the company said this was not because of the campaign.

An actress and novelist, Holmes, 36, began her battle a year ago by launching a petition asking the Sun's editor to address the issue. She was prompted by the contrast in the positive coverage of female Olympic athletes and submissive images of topless young women. It will, Holmes knows, be a long haul and so she feels a connection with her suffragette sisters. "We tend to think, 'Oh yeah, women won the vote'," she said. "We forget about the struggle and how it took years."

Also battling this summer is Banyard, who aims to rid the top shelf of lads' mags and was filming a campaign with actress Romola Garai this weekend. "It's a hugely exciting time for feminism," she said. "It is back in the headlines and back on the streets. The question now is not 'does it exist?', but 'what can it achieve?' The answer to that is up to each and every one of us."

The scale of the task is huge, Banyard adds, as sexism "seeps into every aspect of our lives … What's clear is that change won't come from a small group of policymakers behind closed doors. It takes ordinary people to stand up and make their voices heard."

Perhaps the campaigner with the widest reach is Bates, whose site Everyday Sexism is a platform for thousands of women around the world. She has protested about Facebook's rules about images of violence against women. Limited success so far has been achieved through her approaches to companies that advertise on the site. Nissan UK and Nationwide UK have dropped their ads.

Another campaigner, Megan Perryman, had her epiphany when her five-year-old daughter was browsing in a toy shop. Perryman is now one of the leading voices in Let Toys Be Toys, a British-based campaign that urges shops to stop marketing toys towards only one gender. Her triumphs include decisions by Boots and Harrods to rethink their shop design.

Women have a strong tradition of social campaigning, from the days of Fry, down to Rose Gentle, the anti-Iraq war protester who set up a protest group called Military Families Against the War after her 19-year-old son was killed. More recently, the actress Joanna Lumley and the Pakistani schoolgirl Malala Yousafzai have successfully highlighted political issues.

But for Criado-Perez it is the homegrown issues that still stand out. "I get annoyed when we are talked about as a minority group when we are 51% of the population," she said. She is alarmed too by the fall in the number of women editing national newspapers and the recent decision to give the editorship of influential BBC news shows such as the Today programme and Newsnight to men, although women were in the running. "Employers still think it is enough, under law, to say that they have merely considered women," she said. "In fact they have to show they have also considered the impact of their decision and looked at their criteria."

But battling does not suit every woman. For our first astronaut, Sharman, life in the public eye was deeply unappealing. Refusing to talk about her experiences in space, she once said: "I needed to move on. I am living a different life now." Many feminist campaigners wish they could say the same thing and would long for a time when all women can concentrate, as Sharman once did, on pushing against human barriers and not against those constructed by men.