A Night to Remember by Walter Lord. The definitive 1955 account of the Titanic's sinking, built from interviews with surviving crew and passengers, many still in Southampton. The book that fixed the modern memory of the disaster.
Persuasion by Jane Austen. Austen lived briefly in Southampton between 1806 and 1809, and the late novel is partly informed by the city — the Musgroves' visit to Lyme Regis, the easy familiarity with the Navy. The descriptions of Anne Elliot's daily walks are recognisably Hampshire countryside.
The Empire of the Wolves by Jean-Christophe Grangé. A French thriller set partly in Southampton and the New Forest — pacy if not literary.
Howards End by E. M. Forster. Set further inland in Hampshire but capturing the south-of-England world that Southampton's commercial energy was part of. The "Wilcoxes" are merchant gentry of the kind whose money built the city's Victorian villas.
The Trial of Madame Caillaux by Edward Berenson. A digression: in 1914 the wife of a French politician shot a Paris newspaper editor; the trial in Paris coincided with the start of the First World War. The connection is that the editor's body was repatriated through Southampton, the only port willing to handle the politically tangled cargo. The book is a model of how to read the headlines of a moment as a window on a whole age.