Sardine and tomato is a tin and a tomato turned into a robust sandwich, and the tin is what defines it. Tinned sardines come already cooked, soft, oily, and strongly flavoured, packed in their own oil with their soft edible bones, and the sandwich is built around what that gives you rather than around any cooking. The fish is mashed down, skin, bones, oil and all, into a coarse paste with real fish flavour and real fat, and tomato is folded or laid against it to cut that oiliness with acid and sweetness. It is the assertive, economical end of the British fish sandwich: not the delicate poached-salmon register but a strong, cheap, store-cupboard build that tastes unmistakably of the tin and is the better for not pretending otherwise.
The craft is the mash and the acid against the oil. Sardines are oily enough that no added fat is needed, so they are mashed with a fork to a rough, spreadable texture, often with a little of their own oil, a squeeze of lemon or a turn of vinegar, and pepper to lift the strong fish. The tomato is the structural counter, and it brings water as well as acid, so it is either sliced thin, salted, and drained before it goes near the bread, or mashed straight into the fish so its juice is bound rather than loose. Brown bread is the usual carrier because its closer crumb stands up to an oily, wet filling far better than soft white, and it is buttered to the edges chiefly as a waterproof seal rather than for lubrication, since the fish supplies all the fat the sandwich needs. The point is balance: a sandwich that reads as savoury and sharp rather than greasy, the tomato doing the work that keeps strong oily fish from sitting heavy.
The variations stay close to the tin and the acid. Sardine with a slice of cucumber swaps tomato's sweetness for a cool water-crisp note; sardine mashed with vinegar and onion sharpens it further; sardines on toast drops the second slice for the open-face version. Its near relatives are the pilchard and mackerel sandwiches, the same oily-fish thrift met with a different tin. Each deserves its own article rather than being crowded in here.