The chip butty with mushy peas is the Northern English version of the chip butty where the wet finish is not poured over the chips but laid under them. Mushy peas, marrowfat peas soaked and cooked down until they break into a thick green pulp, go onto thick-buttered soft white bread, the hot chips go on top of them, and the bread is closed and pressed. That order is the defining fact of this build. The peas are a soft, savoury bed that the chips press down into, not a sauce running through them, and it changes the texture of the whole sandwich: where gravy soaks and curry sauce coats, mushy peas cushion.
The craft is using the peas as both the moisture and the structure. A properly thick mushy pea sits like a coarse paste, wet enough to slacken against hot chips but stiff enough to hold them in place, so it does the binding job that loose chips in plain bread never manage on their own; the butty holds together in the hand because the peas are gluing the chips to the bread from underneath. That thickness is also what protects the loaf: a runny pea would bleed into the crumb the way thin gravy does, but a stiff marrowfat pulp largely stays where it is put, and the butter spread to the edges takes care of the rest, sealing the bread against what little moisture works through. The chips go in hot so their crisp edge survives a few bites against the soft peas before it goes, and the bread is plain and soft because the entire filling, peas and chip interior alike, is yielding, and a chewy crust would be the only thing in the sandwich fighting back. A grind of pepper or a splash of malt vinegar through the peas sharpens a filling that is otherwise all soft starch and gentle savour.
The variations keep the chip-and-bread base and change what wets it. Gravy is the thinner, meatier Northern alternative that soaks rather than beds; curry sauce is the sweet coating version. Mint stirred through the mushy peas is the chip-shop refinement, cheese melted into the chips above the pea layer is the loaded build, and mushy peas with a splash of the chip-shop's curry sauce alongside is the hybrid some counters will do. Each deserves its own article rather than being crowded in here.