This is what we found on Wikipedia regarding the Moulin Rouge! The Musical (UK):

Moulin Rouge! The Musical is a jukebox musical with a book by John Logan. The musical is based on the 2001 film Moulin Rouge! directed by Baz Luhrmann and written by Luhrmann and Craig Pearce. Moulin Rouge! is set in Paris during the Belle Epoque; it follows Christian, a young composer, who falls in love with Satine, a courtesan and the star of the Moulin Rouge cabaret.

The musical premiered on July 10, 2018, at the Emerson Colonial Theatre in Boston. Moulin Rouge! began performances on Broadway at the Al Hirschfeld Theatre, in June 2019, with an official opening on July 25. The production was nominated for 14 Tony Awards, winning 10 (the most that year), including Best Musical. Moulin Rouge! continues its run in New York and has been produced for long runs around the world, including in the West End, beginning in 2021.