The bap is the soft option, and that is the entire reason the sausage goes into one. A bap is a round white roll with a yielding crumb and a thin, dusty bloom of flour across the top, baked to be pillowy rather than crusty. It tears where a stiffer roll would crack, and pressed with a thumb it gives and then slowly comes back. That surrender is exactly the behaviour you want under a couple of fried British bangers: the sausage is the constant every region agrees on, and the bap is the variable that names and defines this version of the sandwich. The word also carries a register. A sausage bap is the term you reach for at a café counter or a Sunday-morning kitchen, soft in the mouth and soft as a phrase, where the same sausages in folded slices would be a butty and somewhere a few counties away a barm or a cob.
What the bap does well is take on rendered fat without falling apart. A pork sausage fried until the casing has burnished and the inside has set carries a film of hot fat that has to go somewhere. A baguette would shatter under it and a heavily crusted roll would resist it; the bap drinks a measured amount into its lower crumb, turns slightly dense and rich there, and holds the rest rather than letting it run down a wrist. The build is plain because it can afford to be: the bap is buttered to the edges while still cool so the fat does not soak straight through, the sausages are split lengthways and laid flat so they sit stable and do not roll out on the first bite, and the sauce, brown or red, goes inside against the meat rather than on top where it would run. The flour on the lid stays dry and faintly chalky against the lip while the base has gone soft and saturated, and that two-texture contrast across one small roll is the appeal.
The same sandwich answers to other bread words a few counties in any direction. Folded soft slices instead of a round roll make it a sausage butty; in Lancashire the roll is a barm, across the East Midlands a cob, around Liverpool and Coventry a batch. The fillings stretch the same way the bread words do: a fried egg with a yolk to be managed, fried onions for a sweet counter, the leftover-mash version that beds the sausages on something soft. Each of those deserves its own article rather than being crowded in here.