Tula Paulinea Contostavlos, AKA the singer Tulisa, has a long-running joke with her flatmate, Gareth. (Well, they call it a joke. It sounds pretty stressful.) Every morning, after he has looked through the newspapers and magazines, she asks him who has ruined her life today. Gareth is her former backing dancer, now personal assistant, as well as "best friend, mother and brother", she says, and the pair often sleep in the same bed, entirely platonically, like a glossy, pop-world Eric and Ernie. "I wake up and go: 'Y'all right, Gareth? Who did I murder? Have I still got a career? Tell me. What's going on?'"

At 23, Tulisa's life is more dramatic than ever. Over the years, she has been a carer for her mother, a target for school bullies, a depressed teenager, aggressive teenager, and one third of sparky, scrappy grime-pop trio N-Dubz. Beyond singing, her key task in the band always seemed to be keeping her cousin and front man, Dappy, under control – a job that sounded a bit like wrestling a rowdy octopus. It was all drama, all the time.

Then she became an X Factor judge last summer, and the pressure rocketed. She was suddenly a prime target for the tabloids and gossip magazines; much more famous and potentially much more vulnerable. Stories appear constantly about her love life, looks and diet, which she and Gareth read out to each other in comedy voices. It has been suggested, for instance, that she consumes nothing but cereal and vodka. Not true, she hoots. She doesn't touch cereal. (She likes hot food in the morning.) And, sure enough, in her first months on the X Factor, rumours of a sex tape she had no recollection of filming began to swirl. She went to the producers. Would this affect her job? They couldn't rule it out.

I meet Tulisa a couple of weeks after the footage, which is a few years old, has been released online, and not long after she has responded with impressive chutzpah in a homemade video. In this, she talked about her long-term, serious relationship with the man who she believes released the tape, her sense of betrayal, and her conviction that she has absolutely nothing to be ashamed of. Her response was hailed as an unlikely feminist moment, a woman refusing to be brought low by what she now calls a "fucking stinky situation".

She is here to talk about her first solo single, Young, an upbeat, frothy slice of dance-pop, co-produced by old N-Dubz bandmate Fazer. She knew it had to be the first single, she says, because, "lyrically, musically, it had to be like – boom – here I am, do you know what I mean? And the music had to represent me. So even though it's got that urban edge, it's got an Ibiza edge too, because I'm an Ibiza baby."

Her nickname, The Female Boss, features prominently in the video. The name came about initially because she worked in such a male-dominated environment, she says – in N-Dubz specifically, the grime scene in general. "We used to say if there was any other girl in this group, they would just get walked all over from head to toe. So it became about fighting to survive, and from that to having to dominate the whole situation." She'd have to step in whenever Dappy was having a tantrum, she says. "It would be that intense, every minute, of every day, to the point where I lost my voice practically once a week from the screaming."

The band is on a break now, and she's loving working on her own; she has said, in the past, that it was music that saved her from her teenage depression. She is a genuinely unusual character, open and uproarious, acting out her arguments with Dappy – her screaming, him talking in furious, scattershot sentences – but every five minutes or so, her eyes narrow flintily as she considers a question. There's something weirdly attractive about this. It makes her look harder, shrewder than most of her celebrity contemporaries, much more likely to survive the brickbats.

"I don't really like being vulnerable," she says. "I don't like being weak, I don't like getting emotional, even though I have done in the past. But in general I'm quite–" she pauses, "-not cold." But controlled? "Yeah, very."

Controlled maybe, but completely unpredictable. Talking about music leads us down some unlikely paths. I ask who inspired her, growing up. "Um, you know, I wasn't really one of those fan-ny kids". She sniggers. "Fanny! That sounds wrong, dunnit? You know, like fan. When I was really, really young, I was in love with Michael Jackson. I liked the Spice Girls, the Backstreet Boys, Eminem, and I think once I got past that age of, like, 10, I stopped being a fan of people any more." And started her career? "Yeah!" She has been in N-Dubz since she was 11. We move on to her goals, in terms of the single and upcoming album. She says she wants "to become so successful that if I wanna fart on a track, I can, and it will sell". She laughs explosively. "No, I'm joking! No, my aim is to, yeah, I wanna become a global superstar, I want to become successful enough that I can retire tomorrow in complete comfort. I've made my stamp on the earth, my name will go down in history, and if I never want to work again, I don't have to."

To this end, the album will include strains of hip-hop, R&B and reggae. "I'd say there'll be a song for every scenario you're going through ... If you feel like saying: 'Fuck the world and everyone else,' there'll be a song for you. If you want to say: 'I'm depressed, I want to crawl into a dark hole and die,' there'll be a song for you. If you want to say: 'I'm madly in love with someone and I'm ready to trust again,' or 'Fuck my ex-boyfriend, he's an absolute wanker,' that'll be there."

This last comment seems an obvious nod to former boyfriend Justin Edwards, AKA MC Ultra, whom she suspects of releasing the sex footage of them together (he vehemently denies this). She has obtained an injunction to ban the tape, and is reportedly suing Edwards for up to £100,000 for breach of privacy. When the tape was released, she says, she was "devastated. I slept on the bathroom floor for seven days ... I just wouldn't go out of the house. Couldn't sleep. Didn't really want to eat anything. But I snapped out of it. I knew what I was doing. I knew in my head that I was depressed; I knew why I was depressed. It was all logical. I didn't want to smile. I didn't want to be happy ... It was like a level of mourning, do you know what I mean? I needed to have my tears and tantrums, my bad moods, and get myself into a state to come back out of it. And I literally just woke up one morning, as happy as Larry, put on my best dress, makeup, full hair: 'OK, I'm going out.'"

What cheered her up, she says, was putting out her response. Her management and press team weren't keen. "Everyone was trying to sweep it under the carpet, and I felt that that was making it more seedy than it was. I was like: 'Hang on a minute, I haven't done anything wrong here.'"

So one day she turned off her mobile phone, got out her laptop, made the video, tweeted it, and waited. Half an hour later, she turned her phone back on. "And instantly the response started turning around, once I'd told the truth. Then the headlines were saying: 'Ah, poor Tulisa.' Which was the bloody case, yeah!" She is enraged by those who have criticised her. "I guarantee if everyone else out there had a camera practically shoved up their arse on a day-to-day basis, in their face, that a lot worse stuff would come out ... There are probably girls out there who have done a million times worse with their boyfriend, and are probably going to go out tonight and get laid with a random bloke they've just met, whereas I'll meet a bloke and make him wait six dates before he even gets a shag. But because of some footage, people make assumptions about the sort of character I am."

There have also been suggestions she released the tape herself. There are countless reasons this is nonsensical, she says. There's the fact the tape could have led to her losing her X Factor job (although thankfully Simon Cowell has been supportive). There's the fact it would upset her family. Also, "if I was going to release a tape of myself," she says, "I haven't watched it, because I can't physically watch it, but from what I've heard, I'd make sure I was a lot sexier, and probably not 19 years old, because that's a little bit pervy. People seem to be forgetting that I'm 19 in it, which is quite wrong ... Everything I've spent my whole career building up and representing – I wouldn't even do a bikini shoot with FHM, so why would I release a tape? Why am I spending thousands of pounds in legal costs to stop it coming out?"

We talk about the pressures of her life now: people selling stories about her, paparazzi following her into the supermarket, the gossip magazines printing rubbish about her. "If I could have the tabloids stop writing as much about me, and still get paid the same amount that I do, then I'd be quite happy," she says. "But I suppose it comes with the other things. If I'm not in the public eye, and then I'm not wanted, and I'm not getting endorsements, I'm not being talked about, my records aren't going to be bought. I just wish they wouldn't lie as much."

Tulisa says she doesn't like unnecessary confrontation, but can be aggressive when needs be. Her earliest memory is of crawling along the floor, picking up a bauble that had fallen off the Christmas tree, then attacking the family cat. All her family are performers – her father and uncle were in the 1970s band Mungo Jerry, her mother and three aunts were in 70s band Jeep, and another two maternal uncles were in the chart-topping Irish group Emmet Spiceland. They weren't a rich family. They lived in a one-bedroom council flat in north London, but her dad, Plato, had a little studio, and she first asked to go there to record when she was five. "He picked me up, and held me against the mic, and I sang a song from The Little Mermaid. He said, even then, I did the take, and said: 'Play it back to me.' So he did, and he saw my face twinge at the bum notes."

Her parents split up when she was nine, and she started caring for her mother, who has schizoaffective disorder, which causes serious mood problems. This coincided with a brief happy period at school, and a performance as Tallulah in Bugsy Malone that made her uncle Byron, Dappy's father, prick up his ears. He asked her to join a band he was putting together with best friends Dappy and Fazer, called Lickle Rinsers Crew. "He came to the door, and was like: 'Will you come to the studio?' I was like: 'No. I want to be a solo artist.'" He offered £20. She refused. He offered £50. She agreed. Is money her prime motivation? "No, it's obviously being able to do what I love, while earning money at the same time. But I'm definitely business-minded."

She had her business head on when she met Simon Cowell for the first time, to be interviewed for the X Factor job. "I went to his house in LA, stunning house, sat down, and he strolled in with his sunglasses on, the white T-shirt, and some little dog just running by his side." She swallowed her nerves, and started her pitch. "I said: 'No one's going to bring the realness that I'm gonna bring, because I'm just going to be 100% real, to the point where some people won't like it, but you're gonna get in-your-face raw truth.'"

Still, she was worried on her first day. "I was shitting myself. Oh my God, the first time I walked out, and there's 4,000 people behind you, and every time you try to make a decision, they don't know me, I'm the new judge, replacing their nation's sweetheart, Cheryl ... So I had auditions where people behind me were going 'Boo!', and I'm sitting there with 4,000 people basically telling me I'm a twat, trying to judge someone on stage who probably also thinks I'm a twat." But she isn't one to dwell. The producers suggested she was holding back, so on her second day she told herself to snap out of it. She punches her fist "and it was happy sailing from then ... It's easier to tell the idiots, in the sense of the rude people, that they're bad, because I don't care. And I don't care if they're abusive either. What's horrible is when someone believes they are a star, and they have no vocal ability whatsoever." The act she mentored, Little Mix, became the first band to win the show.

Only the album can answer the question of whether Tulisa can achieve her goal, to become a global superstar, but she has a strong voice, and charisma to burn. She's a one-off; one of the warmest, funniest people you could meet, with a hard-earned capacity to bounce back from heinous situations. But I suspect her future may lie in business. She's a good negotiator, a clever manager, with experience already of working with raw, unruly talents.

She's off to Miami soon to record with producer The-Dream, and seems likely to return to the X Factor later in the year. She says she doesn't trust new people, has a circle of just five friends she can really confide in. But she seems happy, excited about her new songs, and not entirely averse to the drama. Some days, she says, she and Gareth will realise they haven't had any problems for a week, "and we'll be like: 'This feels a bit strange, innit? I'm a bit bored actually.' You have to have the drama so that you can enjoy all the good things, don't you?"