Only government vehicles are allowed to use blue lights and sirens (unless they’re in a museum, on a film set, etc.); I usually see at least two or three cars accompanying important Hungarian politicians (I suppose partly so that if one breaks down, they can switch to another). It’s also possible that there was an official foreign guest in their own car; Hungarian officials don’t usually wave or smile from their cars. It’s very difficult to say, from such a long time ago, exactly what kind of guest was in Budapest at the time—if it was even public info.