The Unfriend is a smart new family comedy which opens on the sunlit deck of a cruise ship. Peter and Debbie, a boring middle-class couple, are introduced to a clingy American tourist, Elsa, who worms her way into their affections. Before they know it, they’ve agreed to let her visit them at home after the cruise. A few weeks later, she shows up unannounced. By now the pair have learned from Google that Elsa is suspected of murdering her husband and several other members of her family. But they’re far too nice, and too English, to tell her to get lost. The crafty Elsa forms an alliance with their angry teenage kids, Rosie and Alex, and uses them to shield her from Peter and Debbie’s suspicions. It’s an amusing set-up and the script just about makes it credible all the way through.

Frances Barber plays the predatory Elsa as a brash, ageing sexpot, like Norma Desmond with a salty hint of Mrs Slocombe. There are terrific performances from Maddie Holliday and Gabriel Howell as the narky kids. And their roles are brilliantly crafted. The dramatist, Steven Moffat, may be over 60 but he knows exactly how teenagers talk and act. Michael Simkins does a hilarious turn as a tedious neighbour who is so lacking in character that no one can remember his name. Reece Shearsmith plays Peter as a numptyish everyman and Amanda Abbington’s Debbie is merely a female version of her husband.

The blandness is deliberate. In this closeted suburban world, feelings are suppressed, conflict is avoided, and obvious facts are dodged and fudged. That’s where the truth of the piece lies. The dialogue is admirably witty and inventive, and there are passages that would not disgrace Noël Coward.

There’s a slight dip in quality during Act Two when a policeman shows up and has problems with a malfunctioning lavatory. The routine doesn’t work because toilet gags have no proper bearing on the play’s central question: what would you do if a serial killer came to stay? It’s fair to reveal that not every character is alive at the end but the timing of the violence is handled superbly. This is what the West End is for. Pure, heavenly escapism.

George Takei is known worldwide as Mr Sulu from the original Star Trek TV series. Now aged 85, he’s the chief attraction of Allegiance, a musical based on his experiences during the second world war. Takei was one of 120,000 Japanese Americans who were held in detention centres following the attack on Pearl Harbor. The show explores the tribulations of the prisoners and their competing political loyalties. Young Sammy, a version of Takei, is a Japanese American who wants to enlist in the army. His father, Tatsuo, a native of Japan, has difficulty resolving the conflict between his motherland and his adopted country. The show is virulently, and even proudly, anti-American. The US guards are portrayed as aggressive, small-minded bullies, and the script invites us to believe that the Japanese are being subjected to monstrous and inhuman cruelties. The truth is that they enjoy nursing care, communal suppers and jazz dances on Saturday nights.

When Tatsuo is asked to denounce the Japanese Emperor, he declines, and so the guards haul him off to a more secure jail. The scene is presented as an intolerable assault on his human rights. But is it? In war, moderation is imbecility. The US authorities would be nuts to allow a foreigner who supports the enemy to roam free while young Americans are dying in battle across the Pacific.

The major selling point of most musicals is a romance between a pair of troubled lovers and this show offers us two couples struggling to keep their relationships on track. Which pair is more important? That’s not clear and the confusion is no help to the poor old play-goer who needs to know where to invest his emotional capital. During a bizarre fight scene, one of the lovers is shot in the stomach and dies. (Needless to say, the weapon is fired by an American guard.) This sudden death erases half the narrative interest of the show. There are better ways to write a great love affair.

The closing scenes re-enact the dropping of the bombs on Hiroshima and Nagasaki but the anguish of the Japanese feels a little perfunctory. The difficulty is that the script is too informative, too well-researched and chronicled. A top-quality musical should appeal primarily to our emotions.

The sets and the costumes are fine to look at. The actors are convincing, with one or two exceptions. It’s hard to say where the audience will come from. Visiting Americans of Japanese heritage, perhaps, if any can be found. The UK’s sparse population of Japanese ex-patriots will turn out in force, naturally. The problem is most of them are in the cast.