It's not every day that a women's rights group from eastern Europe makes it into the Sun. But it's no surprise that the redtop made an exception for Femen last year. Its twentysomething Ukrainian campaigners regularly go topless with flowers in their hair, have worn bikinis made from surgical masks, and even mud-wrestled to draw attention to their cause, since they launched in 2008 – causing outrage among feminists and traditionalists alike. Yet today Femen's almost weekly protests are so successful it is planning to expand into Europe.

Founded by Anna Hutsol, Femen began as a campaign against the explosion of prostitution and sex tourism in Ukraine (sparked by the collapse of the Soviet Union in 1991, and intensified by the arrival of budget airlines and a depressed economy). As its popularity grew, Femen took on issues as diverse as vote-rigging and the stoning sentence meted out to Iranian Sakineh Ashtiani. The next protest, on 26 April, is timed to coincide with the anniversary of Chernobyl when Russian politicians will be visiting Ukraine.

Inna Shevchenko, 20, a spokeswoman for the group, admits no one was listening before they started stripping off. "At the beginning, we were not protesting topless but we realised we had to do something really radical. We don't have people to promote or help us, or big money. Everywhere – from TV channels to magazines – you see naked girls selling something. We are trying to say: 'You should not show your body like that; you should use it to protest and fight.'"

With a pool of 40 topless activists, 300 local members and an estimated 30,000 online supporters, there are now Femen groups in five Ukrainian cities, with plans to set up one in Poland in time for the European football championship next year.

The group's tactics have certainly had an impact, says Ukrainian gender studies expert Tetyana Bureychak. "At the beginning of a lecture on feminism I asked my students what they knew about feminism and what associations they had with the word. One of the first replies was Femen."

Yet many feminists point out that the group's tactics reinforce the idea that women are sex objects whose only value lies in their appearance – a serious issue in a country where the prime minister, Mykola Azarov, felt he could defend his all-male cabinet by saying "conducting reforms is not women's business".

So, it's not surprising that most Ukrainian women are unimpressed by Femen, says Bureychak. "They do not contribute to a positive representation of Ukrainian feminism." However, there is certainly no doubting the commitment of activists such as Shevchenko, who says she has been arrested more than 10 times, lost her government job, and spent nights in jail for her work with Femen. She is one of several full-time activists the group supports through donations and the sale of its merchandise – including pictures painted with their breasts. Like many of the group's members – whose average age is 22 – she is a student in a country where one in eight sex workers is said to be a university student or schoolgirl.

"Men come [to Kiev] in groups of 100 for two or three days and go to nightclubs to pick up girls and do what they want. Before we protested no one talked about prostitution and sex tourism in Ukraine," she says. "But now, all the media here and abroad show that Ukraine is not a country of prostitutes but a country of naked girls fighting prostitution and sex tourism."

Shevchenko blames the economic downturn for leaving women few alternative ways to earn money, and wants the government to take action. "Our government has done everything to develop sex tourism – you don't need a visa to come here. Prostitution in Ukraine is illegal, but in the centre of Kiev there are so many brothels, and the police know about them and do nothing."

Maria Mayerchyk, from Lviv University, stresses that Femen is a "positive, radical and important phenomenon that is able to raise social issues". And Bureychak points out that Femen is operating in the aftermath of a feminist backlash – because gender equality is seen as a socialist preoccupation and too closely linked with the ideals of the Socialist era. As Shevchenko says: "We didn't want to be traditional feminists . . . Women's organisations and groups here only write papers and nothing more. We need activists who will scream and leave their clothes in the street."