The prawn cocktail crisp sandwich has no prawn in it at all, and that is the defining fact. It belongs to the crisp sandwich family, not the prawn shelf: a handful of prawn-cocktail-flavoured potato crisps, the sweet, faintly tomatoey, slightly tangy seasoning that mimics a Marie Rose without any seafood, is laid on soft buttered white bread, the second slice goes on, and it is pressed flat. The reference to the prawn cocktail lives entirely in the crisp's seasoning powder. What makes this a sandwich worth naming is the same thing that powers any crisp sandwich, a hard, brittle, salty crunch trapped between two yielding faces, with the particular joke that the flavour gestures at a seafood starter while containing none of it.
The craft, such as it is, lives in the butter and the press. Butter does the structural work: it grips the crumb and holds the loose crisps so the filling does not cascade out the open edge, and it supplies the fat a dry crisp on dry bread otherwise lacks, which here also carries and rounds the sweet-tangy seasoning so it does not read as thin powder. The press is the technique. Pushing down firmly shatters the crisps in place, binding a loose heap into a single layer that holds for a few bites and delivers the shatter the whole thing exists for. The bread is chosen soft and plain so it compresses to the shards rather than fighting them, and timing is the one real constraint, because the crunch dies fast once seasoned crisps sit against buttered bread and start to soften. It is built and eaten close together for exactly that reason, and the prawn-cocktail seasoning is part of the in-joke that gives the build its specific name.
The variations are entirely in the bag, the same structure wearing a different flavour. Cheese and onion brings a savoury coating, salt and vinegar a sharp acidic edge, and the strongly flavoured branded crisps push the same internal logic into a national in-joke of their own. The plain crisp sandwich is the bare generic statement of the phenomenon without the flavour reference. Each deserves its own article rather than being crowded in here.