Death has been no impediment to opening new shows for lyricist Fred Ebb, who with composer John Kander created the classic musicals Cabaret and Chicago. Ebb died of a heart attack in 2004 leaving Kander to finish the jobs the writing team started.

One of them was The Scottsboro Boys which took the notorious trial of nine African American teenagers who were falsely accused of raping two white women and audaciously framed the story within the style of a minstrel show. It opened to acclaim six years after Ebb’s death, though only four years after his previous show Curtains, which is now receiving its London premiere.

If Scottsboro could not have been more serious, Curtains, an old fashioned whodunnit, feels like the kind of project Kander and Ebb wrote to relax. Were it set on a train instead of a Boston theatre it might have been called Murder on the Orient Express. Here the suspects are not passengers, but the cast and crew of a new musical — with cowboys and hoe-downs — being honed ahead of an intended opening on Broadway. The unexpected climax to one performance arrives when the leading lady is killed during her curtain call.

You could be forgiven for thinking you have walked into a production of Michael Frayn’s farce Noises Off performing a few doors down, at the Garrick Theatre, which finishes its run tomorrow. This is because In both shows much of the action is set behind scenery flats and in the shadowy half-light of backstage. Paul Foster’s production handles these transitions with aplomb.

There is no embarrassment about populating this show with thinly drawn theatrical archetypes, from the vainglorious English director (terrifically played Samuel Holmes), to the hard-nosed producer Carmen Bernstein (Rebecca Lock).

Nor with the coterie of egos that make up a theatre company. Nor should there be. Because with the character of this whodunnit’s sleuth Lt. Frank Cioffi, book writer Robert Holmes has come up with an startlingly original hero — a policeman who loves show biz.

Played with gauche charm by comedian Jason Manford, the Lieutenant is so starstruck by the suspects in his latest case he doesn’t know whether to arrest them or ask for an autograph. Manford is extremely likeable in the role. There is even a whiff of that musical theatre giant Zero Mostel in the gleeful energy with which his Cioffi, who has a slew of am-dram credits to his name, helps his suspects improve their show instead of searching for his perpetrator.

Though the score has won awards it is nowhere near as good as the music that Kander and Ebb wrote for their biggest hits. But this clever love letter to the musical works very well as a fun loving, playful work that deserves its place in the pantheon of musical theatre.

And even though Ebb was 76 when he died, you leave wondering what he might have produced had he lived longer.