Tali Lennox sits on top of the crumpled covers of her hotel bed tugging at her light-brown hair. It’s full of hair pins and kirby grips, something to do with last night’s hairdo for the Scottish Fashion Awards.

"There were hundreds of them in there - there still are," says the  19-year-old fashion model, her face wincing as she plucks out another handful of metal grips. In the bathroom next door, the peach and metallic Nicholas Oakwell couture gown she wore to pick up her Model of the Year award is lying draped over the bath. Lennox shrugs: "It was just too heavy to hang up."

It’s 11 in the morning and Londoner Lennox, the daughter of Scottish singer Annie Lennox and record producer Uri Fruchtmann, only woke up 15 minutes ago. Although the hotel room, which she’s been sharing with her model agency publicist, looks a bit worse for wear (there are clothes strewn all over the floor) Lennox is looking remarkably fresh-faced. "I had a great night’s sleep," she says in her soft, refined English accent.

But didn’t she sleep with  all those hair pins attached to her head? "I did. It was fine. It happens a lot, you get used to it."

Lennox, who has worked for brands including Topshop and Acne, and appeared on the catwalk for London Fashion Week’s golden boy Christopher Kane, is a big deal right now. Her leggy, girl-next-door looks, porcelain skin and enviable cheek bones have won her a series of high-profile jobs. She’s walked in prestigious catwalks shows (Julien Macdonald, Burberry, Alberta Ferreti to name but a few) and is considered a rising star.

She’s picked up a few awards too – three to be exact, including that shiny Scottish Fashion Awards one she received on Monday night. "The awards are surreal, but I try not to look at my modelling career like that – it’s best not to think about it too much because you could end up thinking you have achieved more than you have. It’s always best to go with the flow but I am really appreciative."

Going with the flow seems to be Lennox’s mantra. She says she "likes taking decisions on a whim" and would prefer to let her career go "where the wind takes it" instead of planning out goals. Putting things in the diary seems to be a problem too. "I can’t plan much further ahead than two weeks ever. I was in New York a few days ago for a job and I only found out two days before the job that I was going."

Two years ago Lennox took a leap of faith (encouraged, she says, by both her parents) and left school after sitting her GCSEs to pursue a career in modelling. Although she admits she’s missed out on some formal education, Lennox says the decision has allowed her to grow up a lot quicker. "Maybe I haven’t learned as much about maths but you learn life lessons much quicker."

Lennox isn’t just a pretty face. There are brains behind those striking green eyes. "I’m not a complete thicko," she laughs. In fact she’s a budding artist, with an exhibition of her sketches showing at the Whisper Gallery in London in a few weeks’ time. "I like to be modest about it because I haven’t gone to art school but it’s something I’d love to do. My ambition isn’t just to do modelling. My mum always says that’s what I am [an artist] but I don’t want to get ahead of myself."

Lennox is clearly close to her mother. The M word peppers her conversation. "I still live at home [her parents divorced in 2000] which my mum loves because she still gets to see me." She also loves to borrow from her mother’s eclectic clothing archive. "My mum used to be a big quirky dresser and when I was younger I thought: 'Urgh what are you wearing? That’s disgusting.' Now all the clothes that I borrow come from her."

Close as their relationship might be, Lennox is all too aware of the double-edged sword of having a famous parent. Although a well-known surname opens doors, it can also close minds.

At the beginning of her career Lennox tried to drop her surname altogether. "When I started off I didn’t use a second name, I only went by Tali. Eventually people put two and two together. It’s not like I’m not proud of my mum, but you want the gratification of knowing you’ve done it by yourself. I know people assume that my mum’s name has helped me but I really have worked hard to do it by myself."

Lennox has now accepted that she can be both independently successful and known as the daughter of a world-famous recording artist. The key, she says, is integrity. Her own and also respecting her mother’s. "You don’t do anything that you find tacky – it’s not in my mum’s values, she’s never been into the fame game so I would feel as though I was betraying her if I was really using her name. I would feel like I was disrespecting what she has made for herself."

Lennox also wants to follow in her  mother’s footsteps, and do humanitarian work. She recently visited Sierra Leone with Christian Aid.

"I’ve been brought up knowing about HIV, Aids and poverty in general, because it’s what my mum focuses on. I travelled with her when I was younger so I think that’s what made it less harrowing for me. We visited Aids hospices in South Africa and we saw some pretty shocking stuff, so I guess it set me up to do this. I’d really love to do more of it."

Right now though Lennox has to get ready for yet another modelling job, then it’s back to London to finish her artwork for the exhibition. This summer she’s looking forward to a well-deserved holiday, which she plans to spend with her dad at the Burning Man festival in the Nevada desert. "I go with my dad and his friends, we all get on pretty well. It’s a great festival – you can’t even describe it. But then I love being in really random places."