Media playback is unsupported on your device Media caption Director Sam Mendes told the BBC it was "a privilege" to work on a book he has always loved

Celebrities have turned out in London for the gala opening of the Charlie and the Chocolate Factory musical.

Speaking on the red carpet, Roald Dahl's daughters said their father would have been "chuffed" to have seen his book turned into a musical.

The lavish West End production, directed by Oscar-winner Sam Mendes, is on at the Theatre Royal Drury Lane.

Among the celebrities at the opening night were actresses Uma Thurman, Sarah Jessica Parker and Barbara Windsor.

I feel like I'm one of the lucky children waiting for the gates of the chocolate factory to open. Lucy Dahl

More than 70,000 people have already seen the show since it began previews in May. It is booking until May 2014.

Dahl's much-loved 1964 book, about Charlie Bucket and the golden ticket that takes him on a magical journey through Willy Wonka's chocolate factory, has been adapted for the stage by David Greig, with songs by Marc Shaiman and Scott Wittman.

Douglas Hodge stars as the enigmatic sweet factory boss Wonka, while the large cast includes former Young Ones star Nigel Planer as Grandpa Joe.

Dahl's daughter Lucy told the BBC: "I've come in from California and I haven't seen any of it, so I feel like I'm one of the lucky children waiting for the gates of the chocolate factory to open."

Asked what she thought her father would have made of it, she said: "He never bragged or showed his excitement about things on the exterior, but on the inside he would be very chuffed."

Image caption Sarah Jessica Parker, Matthew Broderick and their son James were among the guests at the gala opening

Her sister, Ophelia, who chairs the Dahl literary estate, said Mendes was ideal to direct the project.

"It's one of the best stories ever and he's one of the best directors ever - so those two things fit together very well."

Both the Dahl sisters recalled attending the premiere of the 1971 musical film Willy Wonka and the Chocolate Factory, which starred Gene Wilder.

Lucy said: "I was about five, and I have a very vivid memory of a massive table covered in a mountain of chocolate."

The stage musical is one of the most eagerly anticipated in the West End this year. It is Mendes' first project since directing Skyfall, the most successful James Bond film of all time.

Charlie and the Chocolate Factory follows the West End success of another Roald Dahl adaptation, the RSC's Matilda the Musical, which won a record number of Olivier Awards in 2012 and this year transferred to Broadway.

According to Mark Shenton, theatre critic for The Stage and the Sunday Express, the big question is whether the new musical can follow Matilda's success.

"Both Charlie and Matilda target the same sort of audience," he said. "Charlie has got a fantastic team behind it, so all the signs are good, but there's no such thing as a guaranteed West End hit."

Charlie and the Chocolate Factory opens in the same week as the Spice Girls musical Viva Forever! closes its doors after poor ticket sales and damning reviews.

Image caption Douglas Hodge plays Roald Dahl's colourful sweet factory owner, Willy Wonka

Also this week it was announced that the critically acclaimed West End revival of the musical A Chorus Line would close early at the end of August.

"Charlie has to worry about a lot of competition in the West End - but to be even half as good as Matilda is going to be a tough job," Shenton added.

The biggest challenge for Charlie and the Chocolate Factory designer Mark Thompson was how to bring Willy Wonka's sweet factory to life on stage.

Speaking on the red carpet, Thompson said that amid the hi-tech scenery he had resorted to some "quite old-fashioned" devices such as the use of projections on a front cloth.

"My aim was to surprise people but also not to unsettle them," he told the BBC. "I want people to leave on a high."