jezbowman, I have flown with several experienced American pilots, and they always shouted "clear prop!"; so I think your experience reflects incompetence on the part of the individual instructor (sic!), rather than a difference between British and American practices.
I was certainly taught to call "clear prop?!" before starting, and always do so. In the Harvards, we call this out before energizing, and call "contact!" just before engaging. The noise of the inertial starter winding up should provide some warning to bystanders; but I certainly wouldn't count on it.
As pointed out
here, if there are any ground crew or other pilots standing near the aircraft, they should visually check that the propeller area is clear and respond "clear", usually with a thumbs up.