As tchrist indicates, it's Mind the gap on UK underground/mainline trains. Presumably by association, our signs usually stick with Mind the step for other contexts where there's a change in level but no gap.
But bearing in mind OP asks whether Watch the step can be used where there aren't any actual stairs, it's worth pointing out that...
[You'd better] watch your step!
...is a very common metaphorical usage as a warning Be careful!, in contexts that may well have nothing at all to do with physical movement (and that one is always your, never the). Note that it's very often used in contexts where the danger involves "clashing with authority" ("Watch your step with the new boss!").
In the literal sense, "the step" can be a step up/down in level where you're walking, or it can be the same as "your step", where it means the act of placing one foot in front of the other to walk/climb. The metaphorical sense alludes to that latter, obviously. Take care with each small move you make.