I was here a few months ago to see Mary Poppins. The Prince Edward was one of two major Cinerama theatres in London, at that time named the Casino. I didn't know that when I was there, but that certainly explains the Cinerama posters displayed in one of the staircases. Here's a shot of the Cinerama screen at the Casino.
See the Coliseum post for an ad when the Prince Edward was the Casino Cinerama.
Inside, the balconies seem reach into the upper stratosphere, which is where we sat for Poppins. When Mary flew over London at the end, it wasn't terribly impressive since we were above her. But I wasn't terribly impressed with the play itself. It's not the books, and it's not the movie but an unsatisfying combination of the two. I really didn't see the need to tamper with the superb Sherman Brothers score by dropping great songs and mixing in some new ones that weren't half as good. However, it does surprise me that it closed -- big musicals (good or not) tend not to just run years in London, they run decades.
As for the exterior, it appears to have been at least partially remodeled.