I wouldn't say that 'john' is one of the most common nicknames for the toilet here, you wouldn't hear it very often. I associate it more with the US, although I could be wrong. Mind you, we don't often call it the 'bathroom' over here either, unless it really is the room that also has a bath in it.
I would be quite surprised to hear "john" in ordinary BrE conversation. I mostly hear "toilet"; often "loo", though not so often from male speakers; occasionally "lavatory"; infrequently "dunny", "bog", "heads", "latrines", "khazi".
I don't really hear "the john" very often either (I think men tend to say it more than women) but I would know immediately what was meant.
Restroom is one of the more common words in the U.S. when referring to a public building.
If you are, for example, in a restaurant, you would say "Where are the restrooms, please?" You can also say "Where's the ladies' room?" or "Where's the