I've also had some great moments drinking tea at Betty's in York.
Last time I was in there, it was at about 7pm (no queue!) and I had some green tea, and a portion of the excellent brown bread ice cream. The waitress was very relieved I didn't ask for it with milk, as apparently there are quite a few people who insist, even with green tea, and they have to do everything to dissuade them...
They do serve a mean cup of tea, whatever kind you drink, however.
(They also did me a rather excellent wedding cake, but that's a whole other story...)
7pm on a Friday is an odd time to visit Betty's - there's something about drinking tea, listening to the pianist play covers of classic pop music, watching York go out on the town (something it does with much gusto) out the huge windows... Before joining them!