The British pulled pork sandwich is an American technique that arrived through the pub and the festival stall and was promptly made to behave like a roll. A pork shoulder is cooked low and long until the connective tissue gives way and the meat shreds under a fork, then it is dressed, piled into a soft bun, and topped with something sharp. What separates the British reading from the source is the restraint applied to the sauce. The barbecue glaze is thinned, used as a coat rather than a bath, and very often pushed aside altogether for apple sauce or a sharp slaw, because the instinct on this side is to cut the fat rather than lacquer it. The defining fact is the shoulder: a cheap, fatty, collagen-heavy cut that is inedible fast and excellent slow, and the whole sandwich is organised around what hours of gentle heat do to it.
The craft is moisture management, because pulled pork has a narrow window between succulent and stringy. Shredded shoulder cools and dries quickly, so it is held in its own rendered fat and a little of its cooking liquor, and the dressing is added at the point of service rather than left to soak the meat into mush. The sharp element does structural work. Apple sauce or a vinegary slaw is not a garnish but the acid and the moisture that lifts a rich, uniform filling and stops it reading as one heavy salty note. The bun is the load-bearing decision and the part the British build takes most seriously: a soft, slightly sweet, faintly enriched roll, sturdy enough to take the fat and the sauce without dissolving in the time it takes to eat standing at a counter, and soft enough to compress to the meat rather than fight it. A bun that goes to paste halfway through has failed the one job it was given.
The variations argue mostly about the sharp counter and the heat. A creamy coleslaw piled into the bun does the cutting with crunch and dairy; a vinegar slaw does it leaner; a spoonful of apple sauce takes it toward the Sunday-roast register; a chilli or a hot sauce pushes it back toward the American end. Crackling shards dropped in bring a hard textural break against the soft meat. The hog roast roll is the close British relative, the same pulled pork carved live with crackling and stuffing rather than dressed from a tray. Each deserves its own article rather than being crowded in here.