The Waldorf. It's in Aldwych. I find it better tha The Ritz. Beautifully done. Reserve a table, get there on the stroke of opening at 3.00 pm, it takes about 2 hours plus. Go without lunch first(!). Chaps, you really need jacket and tie. Sundays there's a formal dance among the palms and the teapots.
http://www.hotels-london.co.uk/hotel.php?hotel_id=3
BTW "High Tea" really implies cooked food and stuff, maybe as far as a steak (but also a pot of tea!). It's a feature of the North of England and Scotland, where it is effectively Dinner, but served early, rather like in Canada, traditionally for when the blue-collar workers got home. Never really a London concept. It's a bit of a dying expression. What the Waldorf, Ritz etc are serving is "Afternoon Tea".