Sofie Hagen no longer tells fat jokes. “I did at the beginning of my career,” she says, a bit regretfully. “Nothing negative, just laughing at myself. I had one joke, where I said something like: ‘I’m fat because I overeat. And I overeat because I have a lot of pain inside. Like, for example, right here’” – she points to her cheek – “‘is a chicken bone I haven’t quite swallowed yet.’”

I laugh appreciatively, but was I supposed to? “It’s really a lose-lose situation,” she says. “I do think there’s something powerful in a fat comedian being visible, owning the stage and calling out what the audience is already thinking. But I don’t make those jokes any more.”

Hagen has a different message now. For several years, the 30-year-old comic has been vocal about what she describes as society’s “deeply ingrained” anti-fat bias and the way it marginalises people, particularly women. On social media, she has highlighted fat phobia in advertising campaigns, inevitably attracting the attention of trolls whose personal abuse can “last for days”.

Some of this abuse, as well as the street harassment she endures, features in her award-winning standup comedy. Hagen’s routines cover everything from politics to boybands. Her outlook and voice – that of an awkward millennial outsider – has pulled in a dedicated fanbase of “quirky feminist introverts, like me”, she says.

Her debut book, Happy Fat: Taking Up Space in a World That Wants to Shrink You, documents her own experiences as a fat child and adult, from crushing weight-loss attempts that were always “95-98% likely to fail”, to dating men who were looking to “settle for a fat girl”. She writes about the problems of flying while fat (do you book two seats or risk not being able to fly at all?); and the “hell” that is summer, with warmer weather bringing chafing, sweat and the increased scrutiny that leaves fat people feeling forced to stay indoors.

When we meet to discuss the book, I have to ask: does she really want me to describe her as fat?

“Yes! I want us to reclaim the word fat,” she says. “I know not everyone likes it. I used to say ‘overweight’. But fat is a neutral word. If you look it up, it doesn’t say good or bad. I want to remove the negative associations, that’s why I put it in the title.”

Happy Fat mixes memoir and political commentary, humour and more difficult moments. There’s her story of visiting a theatre where all the seats had fixed armrests, and having to be seated on a stool instead, “towering over everyone, looking like a lifeguard”. She writes about how food was used to express both love and punishment in her childhood, growing up in Søndersø, Denmark, with her sister and mother. Hagen had little contact with her father, but her maternal grandparents played a large role in her upbringing, and she shuttled between the home of her mother – who forever had Hagen on a diet – to the home of her grandparents, who expressed love through sweet treats and felt insulted if she didn’t eat.

These memories are mixed with statistics, scientific studies and interviews with activists, painting a shocking picture of fat-prejudice and its impact on wellbeing: one survey, for instance, which measured fat discrimination, found that 89% of fat people who had lost weight would rather go blind than become obese again.

Hagen’s book also acts as a guide for women who are overweight or obese to find happiness and learn to accept that their body is – if not beautiful – then, at least, just fine.

This last message is somewhat at odds with the current body positivity movement, which urges everyone to love their body, whatever their shape or size. Hagen recalls speaking on a panel with a prominent figure from the movement. Every time the panellist would say “love yourself”, the crowd would whoop and cheer, and Hagen would respond: “Yes, but how?” Her question only spawned more slogans, more cheers – and no answers.

“Loving your body can feel impossible,” says Hagen, “and just another thing to fail at. You fail at dieting, and then you fail at loving your body. And even if you love your body you might not love it all the time.”

For Hagen, body neutrality, which focuses on respect and acceptance of your body, rather than love, “is something that we can all aim for and achieve ... It’s like my ears. I feel very neutral about my ears. I don’t have bad or good things to say; they’re just ears. And if I could feel like that about my whole body, that would be amazing. Especially as everything within body positivity is based on looks.”

So, for instance, the rise of plus-size models has been seen as a sign of positive change. But Hagen notes that even Tess Holliday – who is “actually fat”, she says, compared to most other plus-size models – “is still incredibly beautiful”.

“People feel uncomfortable talking about beauty privilege,” she says, “but it is part of this discussion.”

Aside from her size, Hagen notes, Holliday is conventional. “She has a symmetrical face, she’s white, femme, able-bodied, long hair. It’s making fatness more palatable, but not really changing anything.”

For Hagen, learning to accept her body wasn’t a drawn-out process; the change came instantly. One day her university friend Andrea asked her to think about where self-hating thoughts come from, and who profits from them, and her whole perspective shifted.

“I used to think – of course fat is ugly, lazy, stupid and bad. I never questioned it. But when Andrea said: ‘You feel bad then you buy more stuff, so they make money,’ it clicked. Overnight I stopped seeing it as a fact.”

This is the political centre of Happy Fat: the argument that fatphobia is a product of capitalism – designed to keep us consuming diet products and miracle foods; and patriarchy – which demands women exert an impossible level of self-discipline around their looks. She sums up the argument with a Naomi Wolf quote: “A culture fixated on female thinness is fixated on female obedience.”

To challenge fatphobia is to challenge capitalism and to see fat people in the context of other marginalised groups. The ideas Hagen discusses come from fat liberation, a grassroots movement that started in 1960s New York and the manifesto of which is included in the book. This includes a demand for “equal access to goods and services in the public domain” and singles out as special enemies “the so-called reducing industries [including] diet books, diet foods and food supplements”.

Hagen says that when fat liberation became body positivity, the movement became more palatable to mainstream culture. “Big clothing companies can make money by saying they’re body positive and that they cater to all sizes, when they only cater to a size 22, and all the people in their adverts are white and perfect-looking, except for a bit of stomach.

“We cannot keep fixing ourselves. We’re never told to look around us. I’m doing panels asking: ‘How do I love myself?’ How about we do a panel with the people who make [fatphobic] adverts and ask: ‘Why did you make that advert?’”

She includes many examples of little acts of kindness throughout the book, including the friends who have swooped in and saved her when she is caught in a conversation with somebody who tells her, unprompted, that being fat will kill her. Then there is the musician she dated, who, realising she might struggle up the many stairs to his flat, stopped every flight for a kiss, to let her catch her breath.

Even the most well-meaning people and those who have suffered marginalisation themselves can have a bias against fat people, she says. One example of how this plays out particularly struck me: telling people they “don’t look fat”. Hagen says this only serves to deny the person’s experience. And it strengthens the belief that fat is wrong. I tell her I am guilty of it myself.

“We all make mistakes. It’s tempting to think of ourselves as good – and therefore not able to be, say, sexist or transphobic – but we’ve all been raised in the same society. The answer is never going to be: ‘Oh, I’m not [prejudiced], phew!,’ because that way we do nothing. We should be saying: ‘I am racist, I am homophobic, I am transphobic and I want to do better.’” She pauses before laughing. “What a quote! I can see the piece now: Sofie Hagen says ‘I am racist.’”

Is it possible to find happiness in your body if you don’t want to dive into anti-capitalist politics?

“For me? No,” she says. “The politics was the main attraction. Politics gave me the desire to want to fight this system so that other people don’t have to fight it any more.”

Happy Fat: Taking Up Space in a World That Wants to Shrink You is published by 4th Estate on 2 May. To order a copy for £11.43, go to guardianbookshop.com. Sofie Hagen’s Bubblewrap, Happy Fat standup and book tour travels the UK from 26 April to 15 June, sofiehagen.com.