In the last few months she has shot campaigns for French Connection and Whistles, featured in British Vogue, Italian Vogue and Wmagazine and appeared in all her naked torso-ed glory with boyfriend William Cameron of Blondelle on the cover of the August issue of ID magazine. There was also that spat when she allegedly replaced Kate Moss as the face of Agent Provocateur.

Whatever the truth, she, and not Kate, is one of their three faces being used in the brand's next campaign.

For such a rock-chick slash super-model you might expect an old-fashioned too-cool attitude but Daisy is all smiles as she says goodbye to the photographer, asks me where I got my top (and really wants to know exactly when I bought it and how much), ruffles her black mane of hair and settles her long limbs into a playful yoga position right next to me on the sofa.

Slightly disarmed by her warmth . . . we had been warned to tread carefully with our questions . . . she reminisces about her good memories of Dublin, having visited here a few times to see Supergrass play. She is in town today to model at a Wrangler fashion event.

We soon move onto the subject of modelling, Daisy having just flown in from London Fashion Week.

"I look obese next to real models!" she says cheekily "Their thighs are the width of my arms. I have boobs and I like my food and I am never going to change that!"

So does she like being a model and is this what she sees herself doing now full-time into the future?

"Ha ha, not really! I mean I feel lucky I can do it, and of course it's all a bit of a laugh pulling poses in front of the camera but I don't like the catwalk stuff at all. Honestly I just see this as a means to doing something else and hopefully that something else will be acting. Sienna Miller was with the same agency and started off as a model, I'd like to do what she did and hop camp."

Daisy did her first shoot for a hair brand at 12 ("it was hideous!") and her first proper fashion job for Agent Provocateur when she was 15. At this point she had already been signed up at Select model agency.

"I was scouted while walking through Camden market . . . they didn't know who I was or what my background was . . . but when I went into the office they booked me immediately. I was actually too young then and had loads of puppy fat so I didn't get any jobs but I am quite driven so I didn't give up. From a very early age I wanted to make my own money so as soon as I finished my GCSEs and was offered proper modelling contracts I went for it. It suited my mum as well as she was sick of me asking for money for clothes!"

What did her mum think when she said she was dropping out of school at 16? Was she worried?

"When I said I wanted to leave school and get into modeling full time I was called home for a family conference . . . I was living with my granny in London while I was in school. I just explained that now is my time and that I just couldn't imagine going to university and ending up in a proper job anyway."

It helped too that Daisy got six As and three Bs in her GCSEs and was tipped for two As and a B in her A-levels. The fact she was leaving school, she says, was nothing to do with not being studious and everything to do with seeing an opportunity and going for it.

"Growing up the way I did, surrounded by so many fashion and music people, I was always going to work in the entertainment industry, it was just a matter of time. Luckily I grew tall enough to be a model but I would have never have had a normal job anyway. Mum never finished school so she couldn't really argue."

With a musical mum, dad and step-dad as well as a boyfriend in a band how about the music industry?

"I try and play the drums but really I am not very good, my foot just can't keep up with my hands!" giggles Daisy. "I can sing though.

When I first got together with Will I used to sing to him all the time but now I am too shy."

So is she shy? Going by the naked cover of IDit didn't look it. "I know that cover was so funny wasn't it?" she says. "Terry [Richardson, the photographer] is a friend for a few years and actually we just felt really comfortable with him, so when he asked us to kiss and cuddle we didn't think anything of it.

Afterwards Will was like 'your granny is so going to kill me!'" "Really though I do get shy sometimes, " says Daisy, suddenly all puppy-dog brown eyes shining through her shaggy Goth-black fringe. "And I haven't always been so confident either. I was actually a really ugly baby!

In fact, I was an ugly baby, a cute toddler a really well-dressed kid . . . my mum was always brilliant with clothes . . . but then there were the lost years between the ages of about nine and 14 when I decided to pluck my eyebrows and do my own hair and really I was hideous! Bad hair, bad teeth, bad clothes, you name it!"

Daisy says it was at this 'geeky' stage she was compared most with her mum. "I started being referring to as Saffy . . . the nerdy daughter from Absolutely Fabulous? So mean!

I hated it!"

Although she isn't shy of the press . . . her 18th birthday was even featured in Vogue ("the reason for that, " she quickly defends herself, "was to get free booze from a sponsor and to have the party paid for! Which didn't work out anyway as the booze people realized they couldn't provide alcohol to under 18s"). Daisy has already grown up to hate paparazzi. "They can come after you very aggressively and I have been chased a few times, it's scary."

So, what does she think of other teenage stars such as Britney, Lindsay Lohan, Nicole Richie and Paris Hilton who were all in the public eye at around the same age as her?

"I feel really sorry for them. I think it's something to do with where they grew up, a sort of Beverly Hills thing. I have an idea for them all which is to build a sort of training camp and round them up and give them lessons on things like how to act in public and how to have a good time. I could teach them that you don't need to go to public nightclubs and get papped every time, that you can invite your friends around to your own place and have a really cool time."

Daisy has been munching the bready bits of a chicken sandwich as we have been talking and lights a cigarette as she sits back comfortably in her white high-waisted Wrangler jeans and black and white blouse, more like a sophisticated woman in her 30s than someone fresh out of school. "I know, I know, " she says "I'm giving up in January, it's a filthy habit."

As we wind down I ask her that old chestnut . . . where she sees herself in 10 years, at the grand old age of 28.

"Oh I'll be married with kids and living in the countryside maybe in France or even in Ireland, somewhere you can see the stars at night." How many kids?

Her famous mum has four. "Ooh I would love about 10, I love kids, but I know that's impractical. Two or three are probably fine!"