Yesterday at dawn the Cutty Sark caught fire and blazed over maritime Greenwich. Timbers shaped in 1869 beside the River Leven caught and flared; decks trodden by sailors in the South China seas smouldered into disaster; intimate, tar-scented spaces which 15 million visitors have explored were filled with hot smoke. Terrible. Eerie, too, for anyone who knows the gruesome Burns poem Tam O’Shanter, whose mini-skirted witch gave the ship her name. That too is about a fire, a witches’ sabbath: “Through ilka bore the beams were glancing,/ And loud resounded mirth and dancing.”

No mirth here. London mourns a landmark, a ship dry-docked in 1954 as a memorial to sailors of the merchant service lost in war or wreck. For more than half a century Cutty Sark has defined the city’s southeastern edges; her slender pencil shape, technologically extraordinary in its day, made her seem to be always in rapid motion. Her soaring masts lifted the spirits. My first child was born in Greenwich, and we often brought the baby to gaze at the scudding clouds behind the yardarms. Through Greenwich’s scruffy doldrum years the Cutty Sark brought the borough pride, and visitors, and identity, just as much as the Queen Anne buildings (and rather more than the infernal Dome).

And she will rise again. Mercifully, the masts, gear, exhibits, figurehead, wheel, upperworks and half the planking were away, in a large two-year restoration project that the Cutty Sark Trust fought hard to achieve. Perhaps the fire will draw still more support, not only for the brave little tea clipper but for all historic vessels.

For there is a special quality in these ships: they are more than interesting exhibits. Perhaps it is because the visitor does not merely look, but travels through them, ducking under beams and climbing narrow companionways as the sailors did. Unlike an historic house, a ship is a confined world: a touching little universe that once held crew and cargo safe in a vast and hostile element. You cannot walk the wide decks or creep the narrow passages of an old ship without imagining how it would be when it lurched and creaked and plunged, week after week, the only man-made object for a thousand miles. You are moved by the humanity, the ingenuity, the blend of professionalism and domesticity in every detail – galley, bosun’s store, charthouse.

Ships fascinate me, and I seek them out more than some; but the remarkable thing is seeing how they appeal to even the most casual visitor. Perhaps it is because of this self-contained, richly human quality, and the small physical novelty of steepness, scrambling and small spaces, but they link you with almost violent speed to the history and diversity of the human struggle. In Oslo I have seen children struck into silence by the ancient grace of the Gokstad burial ship, sacred still in its cool white space. In Long Beach California I have wandered round the Queen Mary, fascinated by the way her curving corridors and Deco details make her feel exactly like her 1930s sister, Broadcasting House. In Mariehamm I have seen the tough practicality of the Cape Horner Pommern, and contemplated the toughness of the great grain races. Moby-Dick came alive aboard the whaler Charles W. Morgan at Mystic, and in Boston I have marched around George Washington’s USS Constitution, which is still towed around the harbour every year to fire a 21-gun salute.

But Britain – because of the passion of individuals and associations, rather than any noticeable government enthusiasm – is richer in these intense ship-moments than most. We have a wonderfully vivid ship-shaped history. At Portsmouth a child can get an instant timeline from visiting the bones of the Tudor warship Mary Rose, then Nelson’s Victory, and finally HMS Warrior: not only the first ironclad but the first ship ever to have a dedicated laundry room for her crew. Visitors take in not only warlike information, but aesthetic: on Warrior you learn how human beings sweetly insist on softening every innovation with retro decoration. The newfangled high-tech battleship had a carved mascot added to her menacing black prow like a ship of 200 years earlier. It was done for sailors’ morale: “Jack likes a figurehead”, they said, and slapped one on, like a teenage girl putting stick-on daisies and Hello Kittys on her iPod.

And then we have HMS Belfast, defining the naval battles of the Second World War, and poor old Britannia recreating the postwar years of spit-and-polish royal tours. Captain Scott’s Discovery is in Dundee, Cold War claustrophobia revives aboard the sinister submarine Ocelot at Chatham, and there are countless Dunkirk veterans and smaller craft all over the country. Each encapsulates some technical, social or commercial moment that shaped our history; each silently enjoins respect for the breadth and energy of human endeavour.

A museum ship has a particular function, teaching maritime lessons to those who would never go afloat, and conserving vital human evidence. Cutty Sark, after all, was only designed to last 30 years and is now 138. If some of her timbers now have to be hewn from fresher wood, so be it. HMS Warrior is no less majestic for having been restored from a near-hulk: I watched the work in Hartlepool, where a skilled team glowed and vibrated with pride, openly expressing their sense of being linked to their Victorian forefathers as they followed their lines and designs.

Richard Doughty, of the Cutty Sark Trust, said sadly yesterday that in the flames we lost “the touch of the craftsmen”. But we are worthy of our ancestors: the 21st-century makers who repair the clipper will, if I know the strange passion these ships arouse, carve as lovingly as the first shipwrights. Let her rise again.

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