Living in London is a charming British tea house that's at the beginning of Santa Engracia street near the Plaza de Alonso Martínez. It's probably the closest thing to an authentic British tea house that you can find in Madrid. The atmosphere is pretty spot-on, especially in winter when the Christmas decorations are up.
The selection of teas is extensive and those with a sweet-tooth are sure to find something they like too (the scones are to die for). Besides tea, there is also a shop where you can get teas and preserves.
It's a bit expensive to be honest, but that's what comes