According to the mid-nineteenth-century miscellany, Chambers' Book of Days:
From time immemorial down to a late period, the 13th of November was annually celebrated, at the town of Stamford, in Lincolnshire, by a public amusement termed a Bull-running. The sport was latterly conducted in the following manner:
About a quarter to eleven o'clock, on the festal-day, the bell of St. Mary's commenced to toll as a warning for the thoroughfares to be cleared of infirm persons and children; and precisely at eleven, the bull was turned into a street, blocked up at each end by a barricade of carts and wagons. At this moment, every post, pump, and 'coigne of vantage' was occupied, and those happy enough to have such protections, could grin at their less fortunate friends, who were compelled to have recourse to flight; the barricades, windows, and house-tops being crowded with spectators. The bull, irritated by hats being thrown at him, and other means of annoyance, soon became ready to run; and then, the barricades being removed, the whole crowd, bull, men, boys, and dogs, rushed helter-skelter through the streets.
One great object being to 'bridge the bull,' the animal was, if possible, compelled to run upon the bridge that spans the Welland. The crowd then closing in, with audacious courage surrounded and seized the animal; and, in spite of its size and strength, by main force tumbled it over the parapet into the river. The bull then swimming ashore, would land in the meadows, where the run was continued; the miry, marshy state of the fields at that season of the year, and the falls and other disasters consequent thereon, adding greatly to the amusement of the mob. The sport was carried on till all were tired; the animal was then killed, and its flesh sold at a low rate to the people, who finished the day's amusement with a supper of bull-beef. . . .
According to tradition, the origin of the custom dates from the time of King John when, one day, William, Earl of Warren, standing on the battlements of the castle, saw two bulls fighting in the meadow beneath. Some butchers coming to part the combatants, one of the bulls ran into the town, causing a great uproar. The earl, mounting his horse, rode after the animal, and enjoyed the sport so much, that he gave the meadow, in which the fight began, to the butchers of Stamford, on condition that they should provide a bull, to be run in that town annually, on the 13th of November, for ever after. There is no documentary evidence on the subject, but the town of Stamford undoubtedly holds certain common rights in the meadow specified, which is still termed the Bull-meadow.
More info at the link. And here is the traditional Song of the Stamford Bullards.
The illustration of the Stamford Bull Running (c. 1800) is from the Kingrock Showdogs website.