Please consider the following room:

The house is a late Victorian townhouse. The room (A) has a size of about 40 sqm, or 400 sq ft., a nice but not elaborate chimneypiece with sofas in front of it, a plastered ceiling, grand piano, a few mahogany pieces. A door (regular, not double or sliding) leads to the dining room, another to the hall.

No television set, which is in another, smaller room (B) upstairs, used for watching television and as a spare guest room. But it's in room (A) that the family sit and read or play board games, in other words, room (A) isn't just for formal entertaining of guests once in a while.

For this sort of room, would upper and upper-middle class Brits say "drawing room", "sitting room" or something else?

Would it be different if the room were used in the same way, but had a desk and lots of bookshelves along the walls?

(I know that there are regional differences and the like, that especially in America, that would be a living room, that many Brits wouldn't fuss and call any lounge a lounge, and that Mrs Bucket would call any sort of "main room" a drawing room, that's why I specifically ask about uppers and upper-middles.)