Very very few, if any.
My upper class ILs (grandparent and great grandparent generation) lived like that until maybe 70 years ago, but though they still have some enormous houses they don't have the liquid cash to run them at the same level. I think the really good years ended shortly before WW2. DH's grandfather definitely had a Bertie Wooster lifestyle.
By 30 years ago, when DH was little, he could leave his shoes outside his room and they'd be picked up, cleaned and returned. By the 2000s they often still had housekeeper, cleaner, part-time nanny, gardener, and at the country house lodge keeper, gamekeepers etc, but most are live-out and part-time. When there's a big event (family xmas, wedding etc) they bring in locals from the village as needed, and bring in caterers for most of the food. DH's grandfather still had a housekeeper who brought the tea service in on a silver platter in the late 2000s. She also was only permitted to use the servant's entrance, but was at the same time part of the family (after serving the tea would sit down and chat and admire the grandchildren), I've seen other much-loved housekeepers and longstanding family nannies seated with important guests at weddings.
They still dress for dinner in some of the houses, though not every night (but might wear tweed, bretons, or woollens as appropriate for the other houses). Cocktails before dinner is still a thing though 
These families are older money though and definitely past their financial prime though still very well off. Not in the same financial class as your tech billionaire, oligarch etc.