On the day of Trafalgar (St Ursula's day, 1805) Edward Pellew was certainly not abed in England. But he wasn't off the coast of Spain. Instead, he was commanding the Royal Navy's fleet in the Indian Ocean, and for the rest of his days he must surely have thought himself accursed he was not there, with Nelson. His career was honourable  in his time he was almost as famous as Nelson himself  but his life lacked the allure of an iconic victory or a poignant death, and today we have almost forgotten him.

Shakespeare would have found satisfying material in the British navy of the Napoleonic wars. There were plenty of striking characters about, ashore and afloat, there was a genuinely heroic strain, and there was an undercurrent of what Churchill allegedly defined as the naval tradition  rum, sodomy and the lash. But this admirable biography of a good man who spent his entire life in the service  Pellew died (in his bed) as the first Lord Exmouth of Canonteign  reminds us that the whole vast construction of Hanoverian admiralty was riddled with rivalry, nepotism, jealousy, opportunism, squabbles over prize-money and petty backbiting.

Pellew was a child of this naval culture. The son of a packet captain, he entered the navy when he was 13 and stayed with it all his life, dying in 1833 as a viscount and an admiral of the fleet. Although a large part of his career was pursued at sea, and although he took part in innumerable minor engagements, much of this biography is necessarily taken up with going-ons behind the scenes.

Pellew was by no means immune to the prevailing navy ethos, but he played it for good as well as for bad. He was perpetually at odds with rival officers, and he shamelessly sought the patronage of the great in search of promotion or advancement, for himself and for his family. His style was sometimes graceless, and although he was often compared with Nelson, he lacked the charisma, spiced with fallible humanity, that was to endear his great contemporary to posterity.

He certainly carried favouritism too far in wangling ships and promotions for two of his sons, who both became not very successful admirals in their time, but he generously pulled wires on behalf of a host of unrelated protégés, too. He did not himself come from a privileged navy family, and he was especially understanding towards young officers of a similar background to his own. His ships' crews greatly admired him, for his kindness as for his ability, and if some of his fellow-officers loathed his guts, many others swore by him.

Much of his sea-time was spent blockading enemies, usually French, in one sea or another, and this often meant ennui. Stephen Taylor skilfully guides us through the less exciting passages of Pellew's life, helped along by a minor scandal or two and many disagreements, and we are made aware always of the man's enviably happy family condition: if he enjoyed an occasional peccadillo on distant stations, he and his wife were successfully married for more than 50 years. He was magnanimous to his French opponents, always considerate to his men, and generally kind.

Pellew fought minor battles in the Great Lakes (during the war of 1812), in the Mediterranean and in the Indian Ocean, but fortunately, from an aesthetic point of view, his two seminal actions come early and late in this book. The first is a small sea-contest that made Pellew famous. It was fought in 1793, at the very start of the French revolutionary war. He was a frigate captain on the Channel station, and after a fierce single-ship fight obliged a French frigate to surrender. It was the first British victory of the war, and it was the making of him. He was knighted, promoted and entertained by George III at St James's Palace; he was presented to the prime minister, William Pitt, and he became a celebrity, the "top gun", as it were, of the dashing frigate captains.

Numerous pages later, the French wars being over at last, we find Pellew, still thinking of Trafalgar perhaps, writing to a friend: "I Have no chance now of being shot and buried in a clean hammock in the pure Element of Salt Water but must be content to be thrust into a dirty hole with the frogs." But the book ends, as it more or less began, with a spectacular triumph.

Nobody describes a naval battle better than Taylor, and he makes the most of the assault on Algiers, in 1816, which brought Pellew to final heights of fame. It was the climax of a campaign against the Barbary States, the semi-independent Muslim princedoms of North Africa, which had for years preyed on the sea-traffic of the Mediterranean, and held thousands of Christian prisoners in slavery for ransom. When Pellew sailed into the port of Algiers with a vengeful fleet of 23 sail, he was, it was believed, fulfilling not simply a British need, but a Christian duty.

It was a terrific action, fought at close range between the warships and the massed guns of the fortified port, and the fury of the battle, the explosions, the fires, the devastation on shore, the whistle of the rockets overhead, was matched by the savagery of a tremendous summer hail-storm. Pellew's success was absolute, and provides a glittering conclusion to his story. The Dey of Algiers was forced into a submissive treaty, and several thousand prisoners, of many nationalities, were set free. It was no Trafalgar, of course, but it did make a lesser European hero of Pellew, and sent him to his grave loaded with the honours of Christendom.

He has never been quite forgotten  his memory is said to live on in the character of Jack Aubrey, the fictional hero of Patrick O'Brian's novels, and it will certainly be revived by this fine book, which seems to me a flawless demonstration of the biographer's craft.

 Jan Morris's Contact! A Book of Glimpses is published by Faber.