A plate of cucumber sandwiches has been the quintessential component of afternoon tea menus since Victorian times. One simply cannot have an afternoon tea from late spring to early autumn without them.
Whenever I make these, cutting very thin slices of cucumber and peeled tomato, I think of a line from the wonderful old Britcom To the Manor Born:
"She serves cucumber sandwiches you don't even have to open your mouth for." ~ Mrs. "Poo" describing Audrey fforbes-Hamilton to her son Richard DeVere
Update 12/07/16: For how to throw an afternoon tea party and a roundup of afternoon tea recipes, see Afternoon Tea Party Tips.
Cucumber Tea Sandwiches
1/8 teaspoon salt
1/8 teaspoon coarsely ground black pepper
64 very thin slices of English cucumber
Optional: peeled and very thinly sliced tomato
16 wide* slices good white bread
About 4 tablespoons unsalted butter, softened
About 4 tablespoons mayonnaise