Bedsitter...never heard the term, but let me guess. The Yank version of that might be an SRO (single room occupncy) hotel? No room for a chair, so you sit on the bed?
I don’t think SRO would describe it although it certainly was a dump, lol! It’s a small flat (or apartment) with a room for a bed and chair. Many students and artists live in them. This was in South Kensington which is overrun with them - at least in the 1970s.
No, in the UK it is common to rent a room in a private homes. Some people rent enough to call them a boarding home.