They've got Rose Tyler surrounded. Shop mannequins have come to life and are closing in on the feisty 19-year-old. "Quick, in here!" A middle-aged man drags her out of harm's way. But before you know it, she's trapped again. This time, in a cavernous sewer underneath the London Eye.

This is the lair of a huge, glowing blob. It is the leader of the Autons, and it means to take over the planet, give evil powers to everything that's made of plastic, and kill all the humans. Now it's Tyler's leather-jacketed hero who needs rescuing. He's been rumbled for carrying a concealed sonic screwdriver.

Two shop dummies have him in a firm grip. Tyler: "I've no job, no A-levels and no future. What I do have is a bronze medal in gymnastics." And with that she launches herself through the air, knocks out the dummies, rescues Doctor Who - for it is he - and saves the planet. Hurrah for Rose, the Doctor's intrepid new assistant!

The new series of Doctor Who offers many surprises. You'll believe a dalek can fly, and that Christopher Eccleston - playing the Doc - can "do funny". And you'll believe Billie Piper can survive a brain-meltingly successful adolescent pop career, a flame-out and a stint as the teenage trophy bride of an ageing media millionaire - and come out the other side, smiling. And rather impressive as feisty sidekick to a sparky but broody Doctor.

Meet Billie Piper, Serious Actor. Who knew? Many people in the television industry, it seems. James Nesbitt, who starred with Piper in her breakthrough role, the BBC's 2003 update of The Canterbury Tales, can't rave about her enough.

"Billie is an original, and has something that's a bit of a cliche - people call it star quality, but it's a very rare aura and presence as a person. That transfers to the screen."

Eccleston - no lover of the celeb side of the biz - told me he clicked with her straight away.

"The camera loves Billie," says Pete Bowker, writer on The Canterbury Tales. "I've seen it before, but never witnessed it so dramatically."

Don't bother telling the starlet herself any of this. "It might be nice," Piper will say airily, to be seen as a proper actor. "But I'm not really that bothered either way. Because as far as I'm concerned, I am a serious actress. I don't need any validation from other people to convince myself that that's what I am."

I've got Billie Piper surrounded. Tabloid journalists - as if teleported by BBC fun-bus from London - have pitched up at Cardiff's St David's Hotel and are pressing in on the 22-year-old.

The occasion is the press launch for Doctor Who, which has been filming in the Welsh capital since last summer.

Piper is encircled by microphone-thrusting hacks, firing questions. She sits there fidgeting with her meshy top, pulling the sleeves over her hands. In her breathy, mild Wiltshire accent, she answers everything.

Last week she was on the front of the tabloids, dressed in her scanties, the pictures lifted from a "glamour" covershoot she undertook for a men's mag. "Dr Phwoar!" said the headlines.

Doctor Who's new assistant, they roared, was - brace yourself - "dalek-table".

Her builder dad in Swindon, unaware that the lads down the building sites were about to cop an eyeful of his eldest daughter, had sent her a text, "Cheers luv!".

It's been a long week. Can she go home now? Quick, in here! Finally a middle-aged man - a BBC press officer - drags her to safety. Piper has survived to fight another day.

Piper has lived in the spotlight "since I left school". Is she aware that one-third of her life has been open to inspection?

"I am aware of it. But also, because I started so young, and I had the pop career before I had my acting career, I'm not in it for fame or money. I'm just in it because I love it."

Even before she married Chris Evans - 16 years her senior - in Las Vegas in 2001 after a whirlwind courtship, Piper had packed a lot in.

She grew up in Swindon, the eldest of four children. At an age when most hormonal kids might want to shun their parents, adolescent Billie Piper "wanted to work like my dad". It was graft, not fame, she was after. At 12, she landed a half-scholarship to the Sylvia Young Theatre School in London, beating 300 other hopefuls.

"I am really excited as I've always wanted to be an actress," she told the local paper then. "This is the first big break for me."

Boarding with relatives in southwest London and travelling by tube on her own was only the beginning of this provincial girl's preternatural self-confidence.

When she was 14, she was cast in a promotional campaign for Smash Hits. "We wanted to find someone who typified the reader," recalls Gavin Reeve, then-editor of the pop mag. "Bright, intelligent, sparky, a bit of attitude. The cool girl in the class. And loads of kids came in - wannabe acting girls with pushy mums, girls who obviously weren't going to be anything. Billie was by far the best."

Piper was spotted in the TV ads and on the cover of industry magazine Music Week by Hugh Goldsmith of Innocent Records, and became the new label's first signing.

Launched in summer 1998 as just "Billie", she would sell one million copies of her first album. Her first two singles went to number one. Aged 15 and 16, she was - and remains - the youngest person to do that.

Relatively speaking, she was more successful than Britney Spears. "I was instantly taken with her. She had that indefinable quality you look for in a star," says Goldsmith. "A combination of a very strong look, very strong features. Almost like a beautiful Manga cartoon character. Huge smile, utterly charming, just a delightful girl.

"But interestingly, when I first met Sylvia, she said Billie's talents were, in reverse order, singing, dancing and acting first. Sylvia said she was a little sad that a singing opportunity had come along and Billie wasn't pursuing her acting career."

Thirty intense months after the release of debut single Because We Want To, and after her second album sold a disappointing (for the mainstream pop market) 250,000 copies, it was all over. Piper had three albums left on her contract but she abandoned her music career. But there still were lurid tabloid tales aplenty.

According to the red tops, she was a wild child who was out of control; she had a tumultuous relationship with Richie Neville of boy band 5ive; she was having abortions here and buying drugs there.

Piper says that ultimately she coped with all the rumours, but appreciates now how hard it must have been for her family. "I mean, I knew that people were saying stuff ... But I really didn't care."

She was similarly carefree, she says, when she was married to Evans and their life of drunken, globe-trotting millionaire leisure was being scrutinised in the press.

She is forthright about their split last year. They were "inseparable for three or four years" but it had run its course. Evans seemed to blame her "back-on-track" career for the break-up. She says that when you're in different places, it's difficult.

Where next for Billie? Is she the next Catherine Zeta Jones? Or, with her film career so far amounting to useless boxing comedy The Calcium Kid, a low-budget British horror film called Spirit Trap, and a failed attempt to land the role Sienna Miller got in Alfie, is Piper destined to be Barbara Windsor for the Noughties?

No, says Pete Bowker. "I don't know that Hollywood quite understands how attractive Billie is and her look. And she doesn't strike me as the sort of person who would go to LA to hang around to get the odd part in the hope of getting a really good part in something like Traffic or Chicago. She strikes me as someone who needs to be working and needs to be doing interesting stuff."

After our interview Piper was driving back to Cardiff for the final four days' filming on Doctor Who.

She's no fool, Billie Piper. She has learned how to perform, how to deal with the cut-throat entertainment business, how to protect herself, and how to move on and thrive.

No, she says, she hadn't wanted to be a pop star. "I was just a huge fan of music, and that's how I like to keep it now. I don't ever want to go back to [music]. It actually gives me the fear just thinking about it."

Now this young veteran watches "Fame Academy and all that stuff and I just think, 'Those poor kids ... "'.

Piper convincingly claims not to be stressed by how big a deal Doctor Who will be. She's done her bit, can't do any more. Like the Autons and the Daleks, we underestimate Piper at our peril.