Egg and bacon is the cooked breakfast reduced to its two load-bearing parts and folded into a roll. A fried egg and a few rashers of bacon are the core of a fry-up, and this sandwich strips away the sausage, the beans, and the rest to commit just those two to bread. The defining decision is how the egg is treated, because a fried egg is a structural hazard the moment it leaves the plate: the runny yolk that works beautifully under a knife and fork becomes a flood in the hand. The breakfast-butty reading of this sandwich is built around managing that yolk against the salt and crisp of the bacon, not around any third ingredient.
The craft is heat, grease, and the yolk decision. The bacon is fried hard enough to render its fat and crisp its edge, since a soft rasher gives the sandwich no texture against a soft egg, and that hot fat is part of what the roll is built to absorb. The egg is the variable: a yolk set firm makes a tidy sandwich that holds in the hand, while a yolk left soft is richer but turns the bread to paste unless it is eaten at once, so the cook is a choice about whether the butty travels or is eaten on the spot. The bread is a soft floured roll, yielding enough to take both the bacon fat and any escaped yolk without falling apart, and buttered so the salt of the bacon carries across to the wheat. The sauce, brown or red, goes inside in a stripe so it does not run.
The variations stay inside the breakfast-roll frame and mostly add one item back. Sausage rejoins the egg and bacon for a fuller roll; black pudding adds a dark, iron-rich layer; a hash brown or fried bread brings a second crisp element. Those deserve their own articles rather than being crowded in here.