It is common stereotype that the British "Tea Time" (after which the tea scene by Carrol Lewis was based) serves large amounts of bread and chocolate. I would recommend eclairs, biscuits, assorted berries and fruit, and various salads, like fruit salad and potato salad, for kids. Traditionally, though, Tea Time served as sort of a second brunch (held at 6:00), using many other less thought-of foods such as Bacon, Bangers (mashed potatoes), Black & White Pudding, Devon Cream, Pasties, Pies, Sausage Rolls, Vegetables and Fish. Basically, these latter ideas are more of a supper, so I really encourage you to use your first idea of sandwiches, and add a little fruit and snacks. You probably already have cake, but just in case you don't, it's pretty common at tea parties. It sounds like a great idea.
A recommendation I'd like to put in for decorations and party ideas: having all the clocks in the room set at 6:00 all the time will represent the punishment the mystical being "Time" put on the Mad Hatter and the March Hare in the first book, "Through The Looking Glass," which explains why he is always having tea. I would make a few comments on Un-birthday parties, and when you give out the treat bags, wish the guests "a very merry Un-birthday." For an extra kick, someone (or everyone, like a costume party) could dress up with rabbit ears or a top hat. A must have would be musical chairs, where everyone is going around a circle of chairs at the main table instead of on the floor, or a cakewalk at the table. Other activities could be riddles "When is a raven like a writing desk?" (even I don't know the answer to that one), or playing cards, (crazy eights, with each card symbolizing a character in the book). The rest of my ideas aren't very good, like revealing the cake out of a giant replica of a hat, but I'm sure you know what to do for the rest. Good luck.