There’s serial music for a serial killer in Adam Cork’s brilliant new score for London Road, a verbatim theatre piece by Alecky Blythe, based on interviews she conducted with neighbours of the man at number 79, London Road, Ipswich, who killed five prostitutes in the last weeks of 2006.

The healing powers of music have rarely been so fulsomely demonstrated as the company of eleven sing their way to living with the past and facing the future, restoring their street to something like normality, in a set of company chorales, rounds and musical meditations.

Cork, who’s best known for his wonderful soundscapes at the Donmar Warehouse and for Rupert Goold – he wrote the music for Enron – really comes into focus in this show, which is ingeniously directed by Rufus Norris on a split set by Katrina Lindsay of coloured panels, a big bay window – housing a six-piece band – and a glorious effusion of flower baskets.

He’s set the dialogue and the interviews to music without any apparent strain, finding rhythm and colour in the Suffolk intonations and everyday idiom – including all the “ums” and “ahs” – light and shade in a television reporter’s stuttering, and building great washes of harmonic sound from even the simplest of statements.

It all amounts to the most genuinely interesting and innovative new musical I’ve seen for ages and cures me of my usual aversion to Alecky Blythe’s method of having actors repeat exactly what they are hearing in their ear phones. They’ve done that, but in rehearsal.

Norris has a hand-picked cast of musical theatre exponents: Clare Burt as a garrulous neighbourhood watch committee member whose husband (Hal Fowler) can’t finish a sentence; Claire Moore and Howard Ward as a blissed out couple, salt of the earth; Rosalie Craig and Duncan Wisbey as retired teachers.

And there’s a real surprise in seeing Kate Fleetwood sing as well as anyone as the gardening spirit behind the floral displays. The level of composition, and musical direction (take a bow, David Shrubsole), is very high. At last we have a really worthwhile, home-grown, experimental piece of musical theatre at the National. Let’s hope London Road starts a trend.