The Tailor-Made Man, Arts Theatre

This stylish, witty musical celebrates the 50-year love affair between the first openly gay film star, William Haines, and Jimmy Shields, a set decorator. It embraces the fashion of the Twenties, the design of the Thirties, the glamour of the big film studios, and the freedom of unconventional lifestyles. A compelling story, fine tunes and some rather attractive actors make for a highly enjoyable evening.

It's a pacey one, too, and Claudio Macor, the writer of the original play (performed several years ago in London and New York) and the director, covers a lot of ground. But the story is clear. In 1922, Haines signed a contract with MGM. The studio accepted he was gay as long as the public didn't find out. When he was arrested for picking up a sailor, the head of MGM, Louis B Mayer (LB), ordered him to marry to save his career. Instead, the actor quit, lived openly with Shields and went into interior design.

Romanticised they may be, but the characters in this show are nicely developed. The dashing Haines is quick with a quip but arrogant; Shields is amiable but sensitive; Marion Davies, a fellow actress and mistress of William Randolph Hearst, stunning, if materialistic; and LB tenacious but paternal (MGM is his family, he sings).

The strongest vocalist is easily Kay Murphy, as the seductive Pola Negri, the actress LB wants Haines to marry, but the leads don't do too badly. Dylan Turner (Mamma Mia!) is an instantly likeable Haines while Faye Tozer (of Steps) brings a comic lightness to Davies. Turner, however, sounds best in harmony with Bradley Clarkson as Shields (pictured, left, with Haines on the right); while Tozer's voice has more depth in the lower ranges. Together, in one of the final numbers, "Design", the chemistry between the three of them fizzes and they sound terrific.

By this point, Haines and Shields are designing homes, and the music and lyrics team of Adam Meggido and Duncan Walsh Atkins have made the song as much about designing how to live a life – what values to choose – as about designing furniture. Their rhymes might not match Cole Porter, but their wordplay is wonderfully inventive. Haines sings of a bedroom door that “swings both ways”; Davies sings wittily of a “flight of Fred-a-stairs”. There are several catchy numbers in this musical, from the lively "Another Party", to the moving "We Got Time". These deserve repeated listens.

Choreographer Nathan M Wright creates a memorable scene with a cluster of picture frames, which are held high, spun on the floor and, at one point, placed over an actor so that they can step through them. The movement is sharp and precise.

The framing device of a reporter visiting Shields in the early Seventies is the weakest part of the show: it threatens to break the magic of Hollywood. But this is a minor quibble. Don't make A Chorus Line your only musical to see in the coming weeks. There's The Tailor-Made Man, too.

• The Tailor-Made Man at the Arts Theatre until 6 April