It is astonishing that it has taken theatre so long to get around to a musical about Frank Sinatra. The seemingly endless desire for jukebox shows has continued in juggernaut fashion for the past couple of decades but, until now, Old Blue Eyes has been conspicuous by his absence. The wait at last is over and now, 28 years after the death of Francis Albert Sinatra, the legend lives again in the West End.

I have seen more jukebox musicals than I care to remember; more recent big-budget examples include the woeful MJ The Musical, which managed to gloss over almost all of the more awkward facts about Michael Jackson’s life. You see, therein lies the dilemma: devoted fans of whichever star is being celebrated want the greatest hits served up without complications, whereas theatre watchers – and critics – as a whole would like some grit in the dramatic mix.

Tina – The Tina Turner Musical ran for more than seven years at this same theatre, the Aldwych, although I found that surprisingly lacking in bite. (Turner, still alive when her musical opened, was too directly involved in its genesis, meaning much scrutiny was not an option.) How, therefore, were they going to treat Frank?

Pretty robustly, is the answer – pleasing and also slightly surprising, given that “Frank Sinatra Enterprises” and his daughter Tina are two of the producers. His womanising, adultery and all-round hot-headedness are central tenets of the narrative, as Joe DiPietro’s script tracks him from the heights of early fame to the “has-been boyfriend of Ava Gardner”, before finishing with one of the great comebacks in showbiz history – Sinatra winning the Best Supporting Actor Oscar in 1954 for From Here to Eternity.