Hathaway, who wore a sequinned brown dress, agreed the film provided a feminist take on the famous story.
She said: "This is Alice 10 years later... when she goes to Wonderland she's experiencing a return to self and I think it's a wonderful take on it."
Depp, meanwhile, dashed up the red carpet to greet his screaming fans in a dark suit and open neck shirt.
Other British voices in the film include those of Alan Rickman as Absolem the caterpillar, Michael Sheen as the White Rabbit, Paul Whitehouse as the March Hare, and Sir Christopher Lee as the Jabberwocky.
Whitehouse, who starred alongside Depp in the BBC's Fast Show comedy series, joked of the Pirates of the Caribbean star: "He's only a two-bit Keith Richards impersonator. Of course he must have been excited to work with me."
Sheen said his character was full of nervous energy, while Rickman said he did not like the story as a child because it was "full of soppy women".
Burton has regularly collaborated with Depp, who has starred in a number of the director's movies, including Sleepy Hollow, Charlie And The Chocolate Factory and Edward Scissorhands.
Burton's partner Helena Bonham Carter also stars in the film alongside Little Britain star Matt Lucas as Tweedledum and Tweedledee.
The premiere, which raised cash for The Prince's Foundation for Children and the Arts, came hours after cinema chain Odeon reversed its decision to boycott the film.
The company said it had reached a deal with Disney over the studio's plan to release the DVD version of the film at the end of May.
It had initially vowed not to show the film in the UK, Irish Republic and Italy as a protest over the plan to reduce the number of weeks a movie is shown in cinemas.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.