In the two months since she won Eurovision, Conchita Wurst has become a global star. Here she reflects on homophobia, gay marriage, Vladimir Putin ('a very handsome man') – and her dreams of winning a Grammy

The photoshoot is in full swing. The starlet is a vision: she flicks her long dark hair, pouts, and expertly twirls her rainbow-coloured couture gown, which swishes around her like a waterfall. "Let's try a sultry one," the photographer says and she turns up the oomph. Lit up by the bay window behind her, she is at once angelic and full-on glamorous. Her face is all fluttering eyelashes and glitter, accessorised with a thick, soft-looking beard.

In the two months since winning Eurovision with the rousing power ballad Rise Like a Phoenix, Conchita Wurst has gone from well-liked personality at home in Austria to global gay icon. Outside, the annual Gay Pride festival is in full swing and the crowd, many wearing fake beards, cheers: "Conchita! Conchita!" She has just headlined Pride in London; Madrid and Stockholm are next. She attended Vienna's star-studded Life Ball, and in Cannes celebrities lined up to be photographed with her ("It was just like, 'Alessandra Ambrosio, of course you can take a picture with me.' It was so, so weird").

In Victorian times, bearded ladies, sometimes genuine, usually false, were a staple of circuses, but when freak shows lost their lure they virtually disappeared. Today, Conchita is a distinctly modern reimagining of the phenomenon: in drag, in control, in 6in tangerine heels. Despite having come straight from the Pride stage, she is fresh and poised: there is no sign of frustration at the long hours, traffic and delays that have marked the day, just concern that her fans had to wait an extra half hour. Immediately warm and welcoming, she is disarmingly coquettish. "It's so nice to meet you," she purrs.

She is still starstruck from meeting Ian McKellen, who introduced her on stage to a packed Trafalgar Square ("I've never been introduced by an actual superhero before"). She was genuinely moved by the fans' reception. "I don't want to say the other Prides are less good, but I fell in love with London immediately, so today is a very special day for me. All the drag queens looked stunning."

Conchita's success may seem to have come overnight, but she has been involved with the music industry for years. In 2007, the elfin and perky 18-year-old Thomas Neuwirth came second in the Austrian TV talent show Starmania. He was then briefly part of a boyband called Jetzt Anders! ("Now Different!"), although they "completely failed. And it was good, actually, because I learned that you have to get up again". Meanwhile, he was developing the stage persona of Conchita Wurst.

Neuwirth grew up watching Eurovision ("I loved it. I watched it with my mum. Back then being on stage was just a big dream"), although he was too young at the time to understand the significance of Dana International, the glamorous Israeli transgender singer who won the contest in 1998. In 2011, Tom became Conchita and made a first bid for Eurovision. Her song finished second in the Austrian competition after Trackshittaz's hip-hop atrocity Woki Mit Deim Popo ("Waggle your arse"), but this year the national broadcaster, ORF, chose Conchita as the country's representative.

When Rise Like a Phoenix was announced as the winner, Wurst was in shock. "Everybody was jumping around, and the golden glitter was falling, and I yelled at my manager, 'René! Have I won this?' And he said yes, and I was like, 'Oh my God!' I couldn't believe it." When they returned to Austria, the country's first victors since 1966, they were greeted by hordes of fans at the airport. In 2015, Conchita will present the song contest in her home country: "It's the 60th anniversary of Eurovision, so I think it's a big deal for Austria to host that. With Austrian history it's good to have something positive."

Conchita's win has ricocheted across the LGBT community worldwide, launching her as an icon and spokesperson. Her eyes open wide as she muses: "It's just unbelievable that nearly every gay human being knows who I am now – that's overwhelming." She is honoured that people see her as a role model, but is concerned about falling short of the responsibilities that come with such a position. "I'm not perfect, I just do what I think is right. So if I can't fulfil people's expectations, I'm sorry, but it's not my fault. I never said that I will change the world. I try to, you know?"

Not all the attention has been positive. Austrians created anti-Conchita Facebook groups, Russians shaved off their beards in protest and church leaders and politicians made disparaging comments about her, variously labelling her "dangerous" and blaming her for fatal Balkan floods. None of this fazes her. "It's funny that these people think I'm so powerful. I've figured out over the years, you can only hurt me if I love you; if I don't know you, I really don't care. There are people who want to kill me and I'm always like, 'Well, get in line, darling.'"

Has being in the public eye ever felt too much? "I don't know why, but no. And I'm thankful, because I'm a very emotional person. I always wanted my life to be like this and I've prepared myself for it."

Despite her vocal support of gay marriage and adoption ("It's so ridiculous and annoying that we still have to talk about equal rights when it comes to this"), she is loath to recognise a political dimension to her work. "The main topic I'm always talking about is equality, and I get that it's politics, but it shouldn't be. It should be the most normal thing ever. There's bullying and discrimination about the colour of your skin, your religion. And it must end." Change, she says, must come at an individual level first: "Most of the time it's just your insecurity that you put on to others."

Russia, in particular, is a topic close to her heart. "Such horrible things happened there, you just want to grab all the gays and take them away. But that's also not the right thing to do, because they deserve the right to live in their own country in peace and harmony."

As an aside, does she have any fashion tips for Putin? "Oh my God. No, not really. I have to say he's a very handsome man. I can separate things, you know?"

Austria's relationship to homophobia, Conchita says, has "totally changed over the years. I believe – deep in my heart – that things get better and better". However, growing up in rural Austria was "a very tough time" for a male teenager who would wear dresses to school. "I thought there was something wrong with me – being gay is not the norm, you're not allowed to do that."

As a teenager, Tom would hole up in the attic to dress up, make clothes and sing. "It was my own little castle. Essentially, Conchita was in the closet and wasn't allowed to go out." When he came out, aged 17, the bullying stopped feeling so hurtful. "For me, the main thing was accepting myself. I said, 'Well, yeah, I'm gay.' And people called me names, and I was like, 'Yeah!'"

His family was supportive when he came out. "They needed a bit of time, but they said, 'We don't care, we love you.'" When he was younger, his grandmother was the first person to buy him a skirt. "We were in this shop and I was yelling and screaming, very annoyingly. So she said, 'Well, get it and we can finally go.'"

Seeing as the relationship with her family is so strong, has Conchita thought about starting one of her own one day? "I don't know; these days, of course not. But my friends and I are between 25 and 30, and especially girls start to think about having babies. I would have to be settled; I'd want the best for this little human being."

Conchita has been a work in progress since Tom started doing drag at the age of 14. "She was always there, but she had no name for a very long time." Her fashion icon is Victoria Beckham, who "does chic like no one else", but Conchita's look evolved organically over the years. "It's like growing up: I've tried every hair colour, every length. But I always wanted to create a glamorous stage persona." Having fun is a big part of it. "You paint your face, you change your look. Every girl in the world should have a best drag friend. Women can get a bit shy when it comes to trying out new things, but with drag I've learned there are no rules as long as you feel comfortable."

Beard aside, the only clue to Neuwirth's gender are the well-defined arms, although they end in carefully manicured, nude-painted nails. The two identities coexist as "two hearts beating in my chest", and have different back-stories: while Neuwirth was born in the Austrian town of Gmunden, Conchita comes from the mountains of Colombia and has a fictional husband, burlesque artist Jacques Patriaque ("a fairytale – he's actually a close friend of mine").

Conchita: ‘I thought there was something wrong with me. Being gay is not the norm.’ Photograph: Phil Fisk for the Observer

Creating an alter ego, similar to Ziggy Stardust or Slim Shady, has been a way of dealing with the pressures of fame and performing. "I can express myself better on stage. It's like Beyoncé maybe with Sasha Fierce or Lady Gaga and her costumes. I think most artists are very sensitive, shy and insecure. And I am too." Conchita is also a way to protect Tom's private life. "I don't take pictures without makeup and most people are nice and respectful. But I hate it when they do selfies with me in the background. That's impolite – just ask."

One of the most common misconceptions about Conchita is that she has had, or wants, a sex change. She is careful to differentiate between drag artists and transgender people ("it's such a serious topic"): becoming Tom again at the end of the day can be a relief. "Like everyone, you're happy when you go home, take off your work clothes and relax. It's a completely different level of relaxation or stress." Although recently Tom has only made appearances in hotel rooms, Conchita says: "I love to be a boy when the wig is off, so I really won't change that."

Rumours have been circulating about Conchita's next career move, whether touring with Lady Gaga ("I wish that was true") or participating in Celebrity Big Brother ("No! No, that's a total rumour"). Instead, she'll be returning to the recording studio to work on an album, which will include ballads (inspired by "mature ladies" such as Shirley Bassey, Tina Turner and Cher) but also more up-tempo numbers. It's no secret that Conchita's long-term ambition is winning a Grammy: "People are like, 'Woah, what the hell is she thinking?' But I need big goals."

And will the beard always be a part of her work? "Well, never say never – if I ever create another stage persona maybe he or she will be without the beard. But I think for Conchita, you know, she's just a bearded lady."

