Front-of-house staff are usually tasked with preventing the filming of shows, with pre-show announcements and prominent signage.
West End stars have also broken character to condemn surreptitious filming, saying it puts them off their performances.
But Kevin Wilson, who has been a publicist for more than 30 years, said that "almost every musical" now allowed audiences to film the finale.
Audiences at the Sister Act musical at the Dominion Theatre are being encouraged to get out their cameras and film the last song of the show.
A message, broadcast at the start of the show, states that while filming the rest of the show is prohibited, people are allowed to record the finale.
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