It's only when I arrive at the cafe where we're to meet that I realise I'm not sure what Kat Banyard looks like. Her anonymity presents an obvious practical problem – but the inconvenience is eclipsed by surprise. How odd to have known her name for years, and not her face – but I think that must be just as Banyard would like it.

Britain's leading young feminist is no Andrea Dworkin sloganist, dramatising defiance via dungarees, nor a gladiatorial Germaine Greer show-off, nor another glossy Naomi Wolf. The young woman who presently approaches is self-effacing, serious and so cautiously considered that I think she can see quotation marks waiting to pounce on every sentence out of her mouth.

I spend the next hour trying to work out what's making her so apprehensive. In the end I decide it can only be fear of allowing any impression that she deserves personal credit for reviving the feminist movement in Britain today. If that's the case, then her nerves make more sense than I'd thought – because I'm afraid there's no way to write about Banyard without doing precisely that. At only 29, she has pulled off what to me at her age had looked impossible, inspiring a fresh wave of feminists without getting into a cat fight with the post-feminists of the 90s, or pretending all the old arguments are boringly obsolete, or having to make herself sufficiently sexy to be media friendly.

UK Feminista, the grassroots movement founded by Banyard, will be marching on parliament on 24 October alongside other feminist groups such as the Fawcett Society, led by Helen Pankhurst, great-granddaughter of Emmeline and one of the Olympics suffragettes. When Pankhurst was recruited earlier this summer, Jacques Rogge was hailing the Games as "a major boost for gender equality", and in the warm Olympics afterglow a mass lobby in protest at the erosion of women's rights had struck some as anachronistic. But since then we have seen the minister for women call for a reduction in the abortion limit to 20 weeks – and the secretary of state for health propose, apparently off the top of his head, a time limit of just 12 weeks. Suddenly the protest could not feel more timely nor more urgent.

"It shows we can never afford to be complacent about the right to an abortion. It's easy to become complacent, and then suddenly we see these attacks, and it brings home how important it is that we maintain a really strong pro choice movement. We need to speak out openly about our own experiences, because these ministers' statements are creating a hostile environment. One in three women have an abortion in their lifetime. The majority of the UK population support a woman's right to choose. All the main UK medical bodies support the current term limit. So it's just not true that the situation has changed in any way. It shows you that women's bodies are still battlegrounds."

It is now 45 years since the Abortion Act was passed. Very few young gay or black people or Muslims or disabled people would say that prejudice had been defeated, yet in the 90s it was commonplace for young women to declare sexism dead. Due in large part to Banyard's activism, this is beginning to change, but why does she think so many women had been convinced they had no need for feminism?

"Throughout the 90s and much of the noughties, we were sold a lie on an almighty scale. That equality had been won, that the battle was over, and now was the time to enjoy our rights. I think what really helped contribute to that was how institutions and corporations who rely on sexism, who rely on women's inequality, adapted and changed. And co-opted the language of feminism very, very cleverly. Feminists of previous generations really got these ideals of independence, equality and agency accepted as standards and values society holds dear. So this didn't escape the notice of people like Hugh Hefner, the sex industry, the beauty industry. They knew that to survive they had to adapt. So all of a sudden putting on makeup was a major route to empowerment; visiting or performing in a lapdancing club was evidence of your independence and how sexually liberated you were. The sex industry held itself up as the promised land of feminism. Everything that feminists had been fighting for – sexual liberation, economic independence, control over their own bodies and so forth. When in fact what they represented was the complete opposite of feminism.

"This neo-liberal ideology of choice being the ultimate test of whether or not something's OK did influence feminism itself, and really threatened to derail the movement. And the consequences are felt by absolutely everyone in society."

The sex industry of today, she says, would be unrecognisable to earlier generations of feminists. "Commercial sexual exploitation has been industrialised, on a global scale, and the profits for a small few at the top – pimps and pornographers – are astronomical." Pornography is literally everywhere, yet in reality "it's a form of filmed prostitution" – and with the average age of a boy's first exposure to hardcore internet porn now just 11, its impact is "an issue we simply cannot ignore".

UK Feminista has worked hard with other groups such as Object to re-categorise lapdancing clubs so they require special sex licences. But the implication of campaigns for tighter regulation of the sex industry, or better conditions for those working within it, might arguably be that it is OK, as long as the women are treated properly. Can there ever be such a thing as an OK sex industry?

"No. There can't. You can't commodify consent. The inherent harm at the heart of this transaction we see evidenced in the astronomical rates of post-traumatic stress disorder, which is a result of having repeated unwanted sex because you need the money. It's often argued that it's just like stacking shelves. That it is ordinary work, just like any other work. But if you're stacking shelves, is it a bit different if your manager says: 'Right, before you go at the end of your shift can you give me a blowjob?' Would you feel uncomfortable about that? It's the inherent harm of having repeated unwanted sex which lies at the heart of the problem."

Banyard regards the sex industry's male consumers as victims too. "I think their sexuality has been co-opted by a predatory sex industry, which distorts and exploits it for profit. A new generation of boys, the vast majority have watched hardcore pornography on the internet, so we have a generation of boys coming through whose first sexual experiences will be vicariously participating in prostitution. They are watching filmed prostitution and getting their ideas about sex from it. This is an industry dedicated to finding ways of getting men to come back and keep coming back for more, so it tends to be increasingly violent to keep upping that response."

Another way of looking at it would be less charitable. Offered limitless choice, it turns out that what men really want is the most violent, degrading, misogynist porn imaginable. Does that tell us something about men?

"Well, increasingly we are seeing men who are speaking out about it." I begin to see how deftly Banyard has learned to sidestep old accusations like man-hating which have tangled up so much past feminist thinking. "One young man, a friend, set up the Anti Porn Men Project because he was using pornography at university, as all of his mates did, and suddenly started to become very conscious of how it was filtering into his everyday life – the way he looked at women, the way he thought about sex, and this really started to jar with his notions of equality. I think that's the only way we'll start to move forward, if more and more men do actually stand up publicly and say this is exploitative, and a man's sexuality should not be based on the exploitation of a woman, and we need to take our notions of sexuality back from these predatory pornographers."

Everyone who has ever campaigned against pornography comes up against the same problem. If they want to stop people using porn, they must want censorship – and what kind of liberation movement calls for state control of individual liberty?

"In terms of what we do about it, I don't think there are simple answers." At first this sounds like a bit of a cop-out, until Banyard points out that our choice need not necessarily come down to a pornographic free-for-all versus nanny state censorship; we just haven't yet had the resources to develop other possibilities. "For me it's really important just to open up that conversation. The organisations that work on this are hugely underfunded, so the ability to conduct research, to provide a forum to develop policy, has been severely restricted. People see it as an inevitable aspect of our life that commercial sex is now firmly embedded in society, and the point is there's an alternative. It's not inevitable. As a society we can choose whether or not it exists."

Post-feminists became a lot more relaxed about pornography when Sex and the City, widely celebrated as porn for women, came along. Now we're all enjoying it equally, the argument went, the problem's solved. Banyard offers a witheringly dry smile. "Well, equality of oppression is never a great strategy for liberation."

A similar argument is often made these days about the beauty industry. With more and more men getting waxed and manicured, surgically enhanced and elaborately styled, why are feminists still so bothered about body image?

"But if you look at the statistics of who is and isn't getting surgery it is 90% women who are having their flesh cut, tucked, pulled, to fit the beauty ideal. Cosmetic surgery fundamentally is about businesses trying to convince people to get unnecessary, invasive, very risky surgery. They know as well as everyone else does that women hate their bodies on a massive scale, and the solution they offer is the knife; they don't say, actually, we need to change the culture which is fuelling the self-hate and making women feel like this. They say, cut up your body to fit the culture."

Some feminists think the solution to a beauty industry that makes women hate their bodies is more diversity. If all sorts of different shapes and sizes appeared in adverts and the media, women would soon stop feeling inadequate – a theory allegedly proven by the sensational success of a Dove ad campaign featuring "ordinary" women. "But it's still this notion that beauty is fundamental to women's identity," Banyard says. "It's still about objectification and commodification. And the product itself they were selling" – a body lotion promising to firm up wobbly flesh – "kind of undermined their claims."

Susie Orbach's public endorsement of the Dove campaign suggested to me tactical feminist pragmatism. To challenge an entire culture of objectification is monumentally ambitious; to make it slightly less damaging is more doable. But it runs the risk of validating the very thing you wish did not exist, so I ask where Banyard sits on pragmatism versus principle. After a long pause and a short, uneasy laugh, she says: "Fundamentally, everybody wants change, and I'm not going to sit here and judge other people's efforts. I do think we need a broad range of approaches to these issues."

I think she's avoiding saying anything that could be misconstrued as a feminist slagging match. "No, not at all. In my book I wrote that I'm seriously troubled by Dove. I think it just shows you the lack of work that's going on to tackle this. It's been completely sidelined as an issue; we don't hear many politicians battling it out on who's going to best tackle the harmful cultures which make young girls feel like they're objects. "I went to a recent event to celebrate efforts to promote better body image, a series of awards, and who got up but businessman after businessman after businessman. For me that's not what a feminist revolution looks like."

Another perennial feminist dilemma is the tension between personal choice and duty to principle. Every woman who gets breast implants can't help but reinforce the message that it's perfectly normal and sensible to spend thousands of pounds being cut open and stuffed with fake breasts. I ask if she thinks feminists who do so are letting other women down.

"It doesn't work like that," she says very firmly. "Not at all. The whole point is that feminism is about tackling the cultures that led women to feel like they didn't look good enough in the first place. I don't believe anyone has the right to judge another woman for the choices she makes in a highly sexist culture. Women have to find ways to survive and get by each day, and how we do that will depend upon our circumstances. I think judging other women on that basis is the antithesis of what feminism is about. And we need to have our sights set on the structures and the industries which feed this culture, who are the ones driving it and reaping the profits from it."

I don't think I've ever met a high-profile activist so lacking in any discernible trace of ego. I've certainly never seen an interviewee approach the photoshoot with greater dread. The modesty makes her a somewhat guarded interviewee – she doesn't like to talk about her private or family life at all – but her achievements are all the more remarkable for it. UK Feminista is galvanising feminist campaigns across the country, training more new recruits in the art of activism.

One critic who reviewed her book complained that Banyard just didn't sound angry enough to stand a chance of making much impact. I wondered if that had made her angry, but she just shrugs. "Yeah, the very notion of anger crops up again and again in feminist discussions; either you're too angry, or you're not angry enough. If you're angry, you're irrational; if you're not angry, you don't care enough." She pauses and smiles. "But I've always found feminism incredibly inspiring."

• This article was amended on 15 October 2012. The original said it was 35 years since the Abortion Act was passed. It is 45 years since the act was passed in 1967.