Robbie Williams poked fun at himself - and fellow celebrities - as he launched his new swing album with a one-off big band show in front of a star-studded audience.

The singer put on an all-singing, all-dancing spectacular at the London Palladium to showcase songs from Swings Both Ways, with guest performances from the likes of Lily Allen, Rufus Wainwright and Miss Piggy.

In what felt like an intimate affair despite the size of the venue, there were emotional references to his baby daughter - who he described as the best thing that has ever happened to him.

There were also celebrities in the audience, with Liam Payne from One Direction, award-winner Adele and comedian Alan Carr watching Williams perform songs from the album, his second inspired by his love of swing.

There was plenty of glitz - with title track Swings Both Ways, a duet with Wainwright, ending with the pair emerging from two glittery closets, wearing shiny pink top hat and tails.

He sang Dream a Little Dream with Allen, who has stayed out of the limelight recently after becoming a mum - and admitted on Twitter after her performance that she had rushed home to her two daughters.

It was the introduction to If Only I Had A Brain, from the Wizard of Oz, that drew shocked laughter from the 1,800-strong audience.

Williams told them: "For a long time, as long as I can remember, I've felt a little bit stupid. I left school without any GCSEs, nothing higher than a D.

"And I'm the first to admit I've made a couple of mistakes.

"Two trips to rehab. Rudebox the album. Geri Halliwell - I should have gone for Victoria really, shouldn't I? I'd have been really famous."

Before starting the song, he added: "Sorry, Geri Halliwell."

There were more jibes directed at himself with a song that involved Williams flying above the audience wearing a padded suit, singing the words: "No one likes a fat pop star".

Williams also unveiled new songs written with his long-term writing partner Guy Chambers, including one that he dedicated to his baby daughter Theodora.

He revealed that the little girl, his first child with wife Ayda Field, reached a milestone recently - and he appeared close to tears as he said: "Thirteen months ago, a very special person came into my life.

"Her name is Theodora Rose Williams and she's my daughter. She's the best thing that ever happened to me.

"I took her to nursery for the first time two days ago. She learned to walk 10 days ago.

"She's the love of my life. I wrote a song about her and this is it."

The song, Go Gentle, featured advice for the little girl as she goes through life, including the lines: "So when you go down to the disco, dancing with young men, just keep it simple - you don't have to kiss them."

There were tears from some audience members as he sung: "Know that I'll be there, I'm going to be there for you."

He mouthed the word "wow" as the song ended, and said: "Thank you folks. That was overwhelming."

The family connections didn't stop there, with Williams' father Pete joining his famous son on stage for what the former Take That singer described as his favourite duet of the night.

The pair sang Do Nothing Til You Hear It From Me, and hugged before Williams senior left the stage to rapturous applause.

Finishing with Mack The Knife, Williams said his dreams had come true after playing at the Palladium, adding: "That was an amazing evening in my life."

The gig was filmed for BBC1 and will be sold around the world, as well as released on DVD.

The new album comes out on November 18.