It's been playing in London since January 1st, 1987. It opened then at the Strand Theatre, and transferred to the Playhouse Theatre, before finally transferring to the Fortune Theatre on June 7th, 1989, and has stayed put there ever since.
By the way, did anyone else know that there was a T. V. film version of this play made? It is extremely rare, and has not been showed on T. V. very often, but it is worth one look. The play is FAR superior, though. You can get a copy of the film off eBay, which is where I got my copy (Mine wasn't a "Unowut".)
MARGARET: "Clara, stop that. That's illegal." - The Light in the Piazza
"I'm not in Bambi and I'm not blonde!" - Idina Menzel