The first rule of Write Club... that you talk a lot at Write Club. Alice-Azania Jarvis meets a London teacher whose secret society has turned curious teenagers on to the power of knowledge

I fancy the Grinch," offers one. "Krusty the Clown!" squeals another. "Bart Simpson," says a third.

This final offering is met with both a chorus of giggles and more than a few murmurs of agreement. Bart Simpson, it is agreed, is hot. We're in the assembly hall of Villiers High School, west London, brainstorming unlikely crushes. My fellow-brainstormers, are 15 schoolgirls. The idea, our mentor explains, is to find someone really odd. Someone no one else will have considered. That's where the comedy comes from.

Said mentor, incidentally, is Caitlin Moran, The Times columnist. She's one of five women invited to spend the day as teachers: each one is given a group, and then does with them (more or less) what they like. While Moran's group consider unlikely crushes (this, she explains, is the subject of most of her columns), another sits on the other side of the hall, writing a song. Their teacher for the day is Tamara Schlesinger, frontwoman of 6 Day Riot. As she explains the different rhyme formations, a gentle love song unfolds. With their lyrics gradually incorporated into the whole, the girls see their efforts transformed into something – if not quite tangible – then at least recordable.

This, of course, is the whole point. "The achievement is two-fold," observes Chloe Combi, the teacher responsible for today's event. "There's the philosophical challenge of constructing something and then there's the gratification of the result." Alongside Moran and Schlesinger are the journalist Ramita Navai, of Unreported World, Stephanie Calman, the author and founder of the Bad Mother's Club, and – much to everyone's excitement – Countdown's Rachel Riley. All women, their classes are all girls; earlier in the year Combi organised a similar event for the boys. Then guests included Nick Hornby and Sean Kemp, the Lib Dems' head of press.

Next up is a plan to host an extravaganza of a day with new and old guests: "It's supposed to be a kind of thank you for everyone who's involved, and a celebration of what we've achieved." The event will mark a milestone of sorts for Combi. These days are the culmination of some 12 months' effort. In 2009 she established Write Club, a semi-secret after-school society offering something more than the didactic prescriptions of the curriculum. She used mystery to capture their attention. Bits of paper started to appear on school noticeboards; featuring stills from a Kenneth Anger film, song lyrics from Leonard Cohen's 'Tower of Song' and esoteric musings, they invited those interested to gather in Combi's classroom one day after school.

The idea was to create a club that triumphed the truism that "knowledge is power". Various weeks have seen students debate philosophy, literature, pop music and cinema. At the start, around 10 pupils regularly attended; now numbers have swelled to 40. "I didn't expect that," says Combi. "Coming after school every week shows such a level of investment. It's great"

Given the success of the project, it is perhaps no surprise that, of the guests Combi approached for today, almost all were willing to get involved. For Riley's part, the opportunity to present maths in a novel, interesting, way was too good to resist. "I try to do as much as I can with schools – especially with young girls," she explains. "There aren't many high-profile women in maths, and it's a shame. It's all about confidence."

Back in the assembly hall, it would seem that she's right. Fifteen minutes into their classes and the girls, in every group, are brimming with the stuff, putting up their hands en masse, keen to make a contribution. "The same thing happens in the club," says Combi. "That's the whole point, really: to give children the confidence to discuss things they wouldn't previously have felt able to."