"change up/down" and "shift up/down" are both OK. "go up/down" also makes sense, but the word choice feels less specifically suited.
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Gene93Change is more frequently used in British English, whereas "shift" is used in AE, is that correct?Some dictionaries say so. I am a BrE speaker, and "change" and "shift" both sound fine to me. I don't know about the use of "change" in AmE. Perhaps an American forum member could comment.
Gene93In the UK, is it uncommon to hear someone say "Shift down at the roundabout." or anything similar to that?It sounds normal to me.