Northumbria once ran from Tyne to Forth, and Berwick was an Anglo-Saxon town inside it. Scotland won the territory at the Battle of Carham in 1018. For the next four centuries Berwick passed back and forth more than a dozen times, taken and retaken by armies that rebuilt the walls every time they captured the town. The Elizabethans, late in the 16th century, finally built fortifications that nobody bothered to take again - the trace italienne ramparts, all angles and bastions, designed against artillery in a style imported from Italy. Most English cities were tearing their medieval walls down by then. Berwick built new ones. Like the walls of Londonderry put up a few decades later, they are now four hundred years old and almost perfectly preserved. You can walk the entire circuit in an hour.

Berwick excels at things named for what they are not. The Royal Border Bridge, Robert Stephenson's magnificent 28-arch viaduct of 1850, does not span the border - the actual frontier is three miles north. The Pier, a 2,877-foot dog-legged structure topped by a 13.5-metre lighthouse of 1826, is not a pier in the docking sense; it is a breakwater, built over rocks, and no vessel can tie up against it. The North Sea looks out toward Denmark from one side, and toward the Royal Border Bridge - that misnamed crossing - from the other. The view east is heaving grey water. Behind you, the painter L. S. Lowry walked these streets often enough to make Berwick one of his favourite subjects, returning year after year to paint the bridges and the ribbon of riverside that runs out to the harbour mouth.

After the Scots were ousted for the last time in 1482, Berwick existed in legal limbo for centuries. Many proclamations referred carefully to "England, Scotland and the town of Berwick-upon-Tweed," treating it as a separate entity. The Wales and Berwick Act of 1746 clarified that England, when mentioned in legislation, automatically included Berwick - settling the formal question if not the felt one. Today the constituency is North Northumberland and the local government is the unitary Northumberland County Council. But Berwick Rangers Football Club play in the Scottish Lowland League. Berwick Rugby Football Club play in Scottish National League 2. The accent shifts noticeably as you walk through town. Locals will say they are Berwickers first and English or Scottish second. The cross-border buses to Eyemouth take both Scottish and English concessionary passes.

The riverside walk is the heart of any visit. Follow the north bank upstream from the pier: first the Old Bridge of 1610, fifteen sandstone arches that James VI and I commissioned at a cost of £15,000, now southbound traffic only. Next the Royal Tweed Bridge, opened in 1928, modernised in 2000, carrying the road that used to be the A1. Last the Royal Border Bridge above, with the East Coast Main Line crossing 126 feet up. A large colony of mute swans patrols the tidal river; despite the name and the location, these are not Bewick's swans, which winter in Britain but prefer the tundra. Walk north of the town on the clifftop path and you reach Marshall Meadows Bay, where the border with Scotland is a stile in a fence. Keep going north for clifftop views over the Berwickshire coast. The Southern Upland Way starts at Cockburnspath, the John Muir Way passes through Dunbar, and both connect Berwick to the long-distance walking network of Scotland.

In December 1966 the London correspondent of Pravda came to Berwick and met Councillor Robert Knox, the mayor, who told him: "Please tell the Russian people through your newspaper that they can sleep peacefully in their beds." Around this real event a modern myth crystallised - that Berwick had been technically at war with Russia since 1853 because Queen Victoria's Crimean War declaration had specifically included "Victoria, Queen of Great Britain, Ireland, Berwick-upon-Tweed and all British Dominions," while the 1856 Treaty of Paris had left Berwick out. None of it was true. The 1746 Act had already settled the point. But the story spread through the Cold War newspapers - The Baltimore Sun, The Washington Post, The Christian Science Monitor - and acquired the embellishment of a supposed Soviet visit and a formal peace treaty. It was nonsense, but it was the kind of nonsense Berwick attracts. A town that has spent a thousand years being claimed by everyone except itself eventually develops a sideways relationship to all official maps.