Well, how about "bank machine" or "teller machine" or just "teller?" There could be human tellers and mechanical tellers. If I'm in a Target store and asking for a "teller" I think they could figure out that I was talking about a machine, not a person. (Actually, I wouldn't care. If they had a person who was willing to give me cash, I'd accept that, too.)

Was "cashpoint" originally a brand name? (Like "Hoover" for vacuum cleaner?) If not, I wonder: who coined that particular term and how it came to be accepted as the standard term?

By the way, I notice that recently "Sharpie" (a brand name) has come to be the common term for what we used to call a "Magic Marker" (another brand name)--a marker in which liquid ink flows out of a porous solid tip.