Cucumber and cream cheese is the tea sandwich that fixes the one weakness of the plain cucumber finger. Cucumber on buttered bread slides: the slices have no grip, and a bitten sandwich tends to shoot its filling out the side in a single sheet. Cream cheese is the answer. Spread on the bread, it is the mortar the plain version lacks, a tacky layer that holds the cucumber in place so the sandwich shears cleanly rather than collapsing. The defining addition here is not a flavour so much as a structural one: a soft cheese doing the job of holding cool cucumber where it was put, with a richer, faintly lactic body coming along as the bonus.
The craft is moisture control, made more demanding by the cheese. Cucumber is mostly water, so the slices are cut thin, salted, and drained before they go anywhere near bread, because the cream cheese will not save a sandwich whose filling is actively weeping. The cheese itself is spread to the edges and serves a double purpose: it grips the cucumber, and it waterproofs the crumb against whatever water the slices still carry, a job plain butter does less well. It is kept to a thin, even layer, since a thick slab smothers the cucumber's clean coolness and the whole point of the pairing is that the cheese supports rather than dominates. The bread is soft white with the crusts cut away, nothing with chew to fight a deliberately delicate filling, and it is assembled close to the table because even drained cucumber softens the bread given time.
The variations are the herb the cheese can carry. Folding chopped dill, mint, or chive through the cream cheese turns a quiet sandwich into a named one, the cheese acting as the vehicle that suspends the herb evenly across every bite. Each of those is a distinct pairing in its own right and deserves its own article rather than being crowded in here.