Though the Watermill’s hugely entertaining show about Doris Day takes its name from her first big hit, A Sentimental Journey, there is nothing in the least bit sentimental about this clear-eyed study of a remarkable show-biz life.

The biggest screen star of her day, who still counts as one of the best-selling recording artists of all time, Doris showed huge versatility both as actress and singer. That her private life was much messier than her ‘girl next door’ image suggested is the major surprise of this well-assembled musical drama.

Writer Adam Rolston and director Alvin Rakoff have achieved a marvel of concision in telling the whole tale — including the four husbands, the bent attorney who ruined her, her fightback from bankruptcy — in well under two hours. That this also includes 20 great songs — divided between all five members of the cast — makes this achievement the more remarkable.

The Watermill’s artistic director Sally Hughes has already had a long stint as Doris on home ground, in London and in Edinburgh. Soon the show is to have a three-week run at the El Portal Theatre in Hollywood. Sally’s affinity with the part is now observable in her every move, her every note, whether in the lilting delight of the title number or the powerful ballads heard later.

While attention is naturally focused on the star, expert work is also done by her four-strong support cast. As her son (now late son), the record producer Terry Melcher, Conor Michael Sheridan also serves, in part, as the narrator. The other actors take on a number of roles. Tom Sellwood supplies a memorable portrait of Frank Sinatra as well as portraying day’s second husband of three years, George Weidler. Nick Waring is hubbies one (the abusive Al Jorden) and three (Marty Melcher, who also exercised a manipulative control on her career). Elizabeth Elvin’s roles include a sympathetic picture of Day’s doting mother, Alma.

Ensuring the show goes with a swing is a four-strong onstage band composed of Jo Stewart (piano), Roger Wilson (clarinet and saxes), Steve Rossell (double bass) and Martin Proctor (drums). A Sentimental Journey continues until October 15 (tickets, 0118 969 8000, www.millatsonning.com)