She has been painted as the struggling waif in the wake of a horrid and very public marriage break-up.

But Cheryl Cole came back with a vengeance last night in her first live show since splitting with cheating husband Ashley.

And as the smiling star performed on the Danish X Factor last night it seemed her cheerful grin could be genuine.

A bidding war has broken out among publishers for the rights to the singer's autobiography, with the price apparently reaching more than £5million.

Smiling again: Cheryl Cole appeared on the Danish X Factor last night as it emerged she could be offered £5m to write her autobiography

Random House, HarperCollins and Penguin are all understood to be among the bidders, with industry insiders claiming competition has grown so fierce that the eventual fee could be the highest-ever paid for a celebrity's memoirs.

The news comes just a day after it was revealed that Tony Blair has received £5million for his autobiography, The Journey, which is due to be published in September.

But sources believe that 26-year-old Cheryl could make even more for her own tale - especially if she decides to reveal all about her marriage breakdown and life as an X Factor judge.

They said many of the publishers consider Cheryl's life story to be a modern fairy tale.

It has seen her escape from a humble upbringing on a Newcastle council estate to become one of Britain's most popular entertainers as a member of pop group Girls Aloud and a judge on The X Factor.

Avoiding the big questions: There was no mention of Cheryl's marriage troubles

Add to that the collapse of her three-and-a-half year marriage to Chelsea footballer Ashley Cole after he was alleged to have cheated on her with at least four other women, and you have a potential bestseller.

However, the offer still represents something of a gamble. Although celebrity memoirs often come with large advances, very few sell more than a few thousand copies.

Jonathan Ross is believed to have received £1.5million from Bantam for his memoirs Why Do I Say These Things? However, since its publication in October 2008, the book has sold just 139,500 copies.

All smiles: Cheryl told the 2m audience 'I'm happy to be here'

Cheryl's spokesman insisted she had 'no plan' to write an autobiography.

The singer is said to be preparing to meet her estranged husband next week for last-ditch talks about their future.

She has issued a 'hands-off' warning to Cole, telling him not to hug her when they meet as she does not want to be distracted from what he has to say.

Last night she gave an accomplished rendition of Fight For This Love in Copenhagen that betrayed no hint of inner turmoil.

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Two million Danish viewers watched Cheryl bound on to the stage in a military inspired outfit, unbuttoned to show a large amount of cleavage, with a police-style hat.

She sang Fight For This Love - the lyrics of which are now only filled with irony.

And of course no wedding band was missing also. She has not been seen wearing her wedding ring since February 9 - almost a month ago.

The 300-strong crowd in the TV studio wolf-whistled and gave her a standing ovation.

She told them: 'Thank you very much, it's a pleasure to be here. To be No.1 is the goal. It's the best feeling in the world.'

She added: 'Everything's good. I'm rocking it and enjoying myself.'

Hard at work: Cheryl and her six dancers performed Fight For This Love

Cheryl joked she would be letting her hair down after the show. 'If there's a party I'll be there. That's what it's all about. I'll show you my moves, don't you worry.'

Asked how she was feeling, she said: 'Everything's good. I'm OK'

The performance came as the Mail learned Cheryl has also dropped her married surname Cole in favour of her maiden name Tweedy during her current promotional trip to Europe.

Her first class British Airways flights between London Heathrow and Copenhagen were booked under the name Cheryl Tweedy.

Cheryl also did not book into the Danish capital's only five star hotel - the First Hotel Skt Petri - using the name Cole despite her being virtually unknown in the country.

Energetic: Cheryl gave a storming performance in her daring military outfit

It emerged last night that Cheryl never changed her name to Cole on her passport and indeed is intending to fully revert to using the name Tweedy if a divorce from Ashley cannot be headed-off.

Cheryl's spokesman confirmed to the Mail that she has not been using her married name on the trip but played down its significance claiming it was merely for bureaucratic and security reasons.

He said: 'Cheryl's name on her passport is Cheryl Tweedy which is why flight was booked under that name.

'Her passport was not changed when she married Ashley. As for the hotel booking, it is always made under an alias. All pop stars do the same and she was doing that when she was in Girls Aloud as well. This is standard practice.'

The carefully-worded response also gave an interesting hint about the apparent demise of Cheryl's place in the girl band.