We don't, that i know, have family rooms or dens in the UK, but i have always been a bit confused by the possibility of both living rooms and sitting rooms. There are also lounges, of course, but the kind of people who have lounges certainly don't have sitting rooms. To say nothing of drawing rooms.

There's actually quite a good gallery of British living rooms through the ages in the Geffrye Museum in London, starting from back when they were called parlours. The main thing i remember about it is that the Victorians had fantastically poor taste in interior decoration.