Ian is the chairman of Live Nation, producer of both the current West End revival of Guys and Dolls and of The Producers.
Until recently Live Nation was known as Clear Channel Entertainment, an offshoot of Clear Channel Communications.
It is the first time a new entrant has headed the top 100 list. Producer Cameron Macintosh takes second place, while Lloyd Webber has been bumped to joint third, tying with Howard Panter and Rosemary Squire, the founders of Ambassador Theatre Group.
The list's top 20 includes Old Vic Artistic Director Kevin Spacey, Donmar Artistic Director Michael Grandage and Nobel Laureate Harold Pinter.
In 20th position, two of the list's most notable entrants are David Babani and Danielle Tarento, co-producers at the Menier Chocolate Factory, whose current production of Sunday in the Park with George has been extended by three weeks until March 12, 2006.