The Liar's Daughter, By Laurie Graham. Quercus, £16.99

Ronan Farrow joked that "we're all possibly Frank Sinatra's son", when his mother Mia suggested that he could have been fathered by the singer, not Woody Allen. But James Joyce's famous assertion that "paternity is a legal fiction" has far-running consequences. Especially when aligned with celebrity, as Laurie Graham's latest novel shows.

Nan Prunty believes she is the daughter of Admiral Nelson. That's what her mother, Ruby Throssel, a once boyish-looking young woman who worked on ships, has always maintained. Her mother was present at Trafalgar and helped ease Nelson's pain when he was dying. But surely the drunken, lascivious, amoral Ruby, who sold her daughter into prostitution when Nan was only 14, can't be telling the truth?

After Nan is given a proper education by a kindly old gentleman and finds work with an apothecary, she meets a young doctor, Archie McKeever, who wants to marry her. His scepticism about her mother's claim makes Nan determined to find out the truth and so the narrative thrust of the book – a search for a father – begins.

What Nan discovers on her long journey through the history of Trafalgar is that many people lay claim to have been fathered by Nelson. And there are some who prefer to think they weren't fathered by him at all, like Horatia Ward, adopted by the admiral and brought up by his mistress, Lady Hamilton. Was Horatia really Nelson's true daughter? She doesn't like to think the great man could have been so indiscreet. Nelson is a great hero, and great heroes don't go siring illegitimate children all over the place.

Graham's empathetic and entertaining novel takes a different turn when Nan's daughter, Pru, grows up to become a nurse. Like her grandmother, she soon finds herself at the scene of battle – Sebastopol – tending the injured and dying. It's a neatly squared circle, if a little less compelling, but it shows that searching for a father may mean meeting the mother you thought you knew, as if for the first time. Maternity is a different kind of fiction from the "legal" one.