I’ve been meaning to post this for some time, as it was new to me. Now Lynne Murphy (?) has written about it in separated by a common language. She says that the British use the term peanuts only for the shelled variety, and monkey nuts for those in shell (her picture is borrowed from yak).

I think it must be a recent development. Monkey nuts has always been colloquial, and I would have said not specifically for peanuts in shell. The OED gives some examples from 1880 on, but doesn’t say anything about a specific meaning. Maybe some advertising wizard hit on using it commercially?
How about tiger nuts? And then there’s the monkey-puzzle tree, quite common in front gardens.