Finger sandwiches in Boston / Boston-north area?
If you are looking for a place that serves tea and those sandwiches I can't help, but I have a (no longer) secret love for the overpriced but delicious finger sandwich boxes at Japonaise bakery in Brookline. They have ham ,tuna, egg, turkey, and all of those on wheat or white, but the end result is much better than it sounds. Crust trimmed off, cut into rectangles, and ready to go. yummm. Grab a ham and cheese croissant or melon pan or even one of thier lovely cakes and you're all set for tea on your own terms.
I believe Japonaise also has them at their smaller outpost in the Porter Exchange building in Cambridge. I don't think they have cucumber sandwiches, though.
And as Zatan said, anywhere that serves afternoon tea will serve finger sandwiches. A board search along these lines will yield many hits, but a few of the old standbys are the Taj, the Four Seasons, and the Park Plaza.