On a recent trip to London, after lunch at the Wolseley, I took my teenage daughter to the Ritz just to show her the dining room, which I genuinely think is the most beautiful in London. I was not wearing tie, but did have a jacket (I think). The maitre'd was charming and welcomed us into the dining room, and was not snobby at all, which was appreciated. I think it helped that my daughter is very charming in turn!
I've never actually dined there, so can't comment on the food, but I think it's fine that some "old school" institutions exist: it's the minority++ of places, and it's good to have diversity. Dining isn't just about the food (or the abhorrent insta-bait presentation that has overtaken restaurants).
tb