They included Les Miserables, The Wizard of Oz and Billy Elliot, Webber's trial heard.
Billy Elliot's other nominations include best new musical and best director for Stephen Daldry.
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Billy Elliot, the Musical is based on the 2000 Oscar-nominated film which starred Jamie Bell.
Billy Elliot director Stephen Daldry will direct the West End production next February at London's Gielgud theatre.
It was recently reported that Billy Elliot star Jamie Bell was set to succeed Radcliffe in the role.
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The "Billy Elliot" cast didn't perform the whole show, only a couple of numbers, but that didn't seem to matter.
Bell became an international success with his screen debut as a ballet dancing youngster in Daldry's Billy Elliot three years ago.
Stephen Daldry, who directed Bell in Billy Elliot and has remained good friends with the young star, was also among the guests.
More recently, a "Billy Elliot" tour had to close after one year because it couldn't sell enough tickets to fill an overbooked schedule.
It was his work as a choreographer on "Billy Elliot, " preparing young performers for a starring role on Broadway, that helped him conquer his own fears.
The "Kinky Boots" haul did not match the record number of nominations for a musical, which is 15, set by "The Producers" in 2001 and "Billy Elliot" in 2009.
"It would be easy to call it the best British musical since Billy Elliot, but that, I'm afraid, would be underselling it, " said Richard Zoglin in TIME Magazine.
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"I have been blessed in my life to spend the majority of the last 10 years of my life working on the story of Billy Elliot, " said Daldry, calling it a "long, extraordinary journey".
The pair cite British films like Brassed Off, Billy Elliot and The Full Monty as examples of what they hope Untouchable will achieve, having more to say on a social level than simply making people laugh.
The move by the Tonys seems strange since the three boys rotating the lead of "Billy Elliot the Musical" David Alvarez, Trent Kowalik and Kiril Kulish all took home a joint best actor Tony in 2006.
It has been nominated again this year and is up against Billy Elliot the Musical, The Phantom of the Opera and Wicked for the BBC Radio 2 Audience Award - the only Olivier voted for by the public.
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Billy Elliot, which is set in a poverty-stricken British town in the 1980s and tells the story of a young boy discovering his love of dance, has been one of the most popular musicals since it debuted on Broadway in 2008.
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