For a period in the early 2010s, it was impossible to turn a newspaper page or open any form of social media without seeing the voluptuous eyebrows of Cara Delevingne and, beneath them, her tongue sticking out of her mouth, giving off a manic puppy energy. She’d make gang signs despite growing up in well-heeled Belgravia, and wear beanies at slouchy, Smurf-like angles. Delevingne became a sort of lovable if OTT caricature, one her friend Kate Moss captured perfectly when she dressed as her for Halloween. This ubiquity wasn’t entirely Delevingne’s fault. What 20-year-old thrust into fame and (even more) fortune would not take advantage of the endless work opportunities, invites and access that came her way? And even more so: we have a media that will see any new thing, especially if that thing is young and female, and hound it, in some cases, to death. These days, Delevingne is a rare presence on catwalks, but has branched out with acting (Suicide Squad, Paper Towns) and singing (backing vocals for Fiona Apple). She’s designed capsule collections for Mulberry and DKNY, launched her own brand of prosecco and invested in a sex-toy company. It is that, combined with the fact she was once photographed carrying a giant BDSM sex bench into her home, which means that her fronting a documentary called Planet Sex is not as outre as it might appear. Planet Sex arrives on Thursday on BBC iPlayer. The first episode, centred on female pleasure, has garnered the most attention, probably for the detail that Delevingne “donates” an orgasm to a research lab in Germany, which rather conjures up an image of her struggling along a strasse with a giant climax in a bin bag. As it is, she has a wank in a sterile room then has her bloods taken, whereupon a husband and wife scientist team tell her the results show high levels of endocannabinoids. In layperson’s terms, this means that coming makes you feel good. Hardly a revelation. (Or it may be, to the 35% of straight women Delevingne tells us do not experience orgasm during intercourse.) In New York, Delevingne visits artist Sophia Wallace, who makes giant, anatomically-correct models of clitorises. They look a Jeff Koons, if Jeff Koons made wishbones, but in a good way. There’s a low-lit sex party at which multiple women lick the salt for their tequila shots from Delevingne’s thighs, which is not something you get with Adam Curtis (though there is a similar amount of rocket-launching archive footage). Delevingne is curious and enthusiastic throughout, imbuing the script with a sense of fun, and charming the experts and case studies. She’s an entertaining fourth-wall breaker, and evidently keen to learn and explore. There’s a fascinating episode (the third) on porn addiction and what it does to people’s brains, which includes input from the ever-articulate Make Love Not Porn founder and educator Cindy Gallop. But it is episode two which stands out as a genuinely affecting and brutally honest piece of television. During Delevingne’s rise to fame, she was in a two-year relationship with the musician Annie Clark (professionally known as St Vincent). It seemed a slightly odd pairing; the cerebral, New Yorker-profiled Clark with the goofy young model, but it was uplifting in its prominence. More often than not, female same-sex relationships exist in the fashion and music worlds as titillating PR stunts or fetishism-as-accessory; yet here was a for-real couple on the front rows of Paris and London. It was a big deal. But if one had the impression that Delevingne found this openness easy, Planet Sex makes it clear it was – and continues to be – no such thing. As well as potentially jeopardising her career (still! In 2022!), coming out in the public eye, Delevingne tells us, meant that she did not get a chance to “develop her queerness”; she has never been to a Pride event. To correct this, she visits the notorious lesbian bacchanal that is the Dinah Shore weekend in Palm Springs, California, splashes with lots of half-naked women in swimming pools, and has a blast (“I have gay friends now!”). She speaks, too, about internalised homophobia, which is increasingly taboo in a world where people can’t just be OK with their bodies, but have to be “body positive”; can’t merely admit that they have mental health issues, but have to extol the virtues of ostensible benefits. Delevingne does not second-guess anything she says, and it is incredibly refreshing. On more than one occasion, she worries that she’s “not human” and mentions past suicidal ideation. On another, you see her, in real-time closeup, come to the conclusion that a particular habit she’s developed is unhealthy. Those eyebrows furrow. It’s basically a 45-minute exposition of shame, and I’m not even sure Delevingne realises how brave or bold she’s being. (She is also very funny. On the high retirement population of Palm Springs: “What do I know about Palm Springs? It’s hot, it’s a desert. And it’s where old people go to die.”) While Delevingne plus sex was never going to be a hard sell, presenting is an area that comes naturally to her. She’s self-aware enough to tease herself about “going on a journey”. And yet, she has said that making this series changed her life. So often, this is the kind of baloney celebrities come out with when they’ve popped to a famine-struck country for a weekend, or in this case, hung out with a Buddhist monk drag-queen. But throughout Planet Sex, there are moments that are disarming in their emotional candour and intelligence – and others where revelation almost audibly clicks. In the UK and Ireland, Samaritans can be contacted on 116 123, or email jo@samaritans.org or jo@samaritans.ie. In the US, the National Suicide Prevention Lifeline is 1-800-273-8255. In Australia, the crisis support service Lifeline is 13 11 14. Other international helplines can be found at befrienders.org.