That looks like a fantastic example of what those driving-test hazard perception things should be like (not having done one myself, I can't say if they're actually like that - is the Driving Instructor around here, perhaps he could advise?). The opening shot is of zebra crossing and bus. For any driver that should ring an alarm bell. The bus is obscuring the start of the crossing - you can't tell if it will be safe to cross the crossing until you can see either end of it. So you MUST slow down to a speed at which you can safely stop should there be a pedestrian on the crossing. This applies to any driver, whether driving an emergency vehicle on blues & twos or not. The fact that any pedestrian might hear you coming and choose to wait is beside the point - you still need to be prepared and able to stop safely if necessary. Incidentally, as a pedestrian crossing that crossing, if there were no sirens going I would have walked out only far enough to check that any oncoming vehicle was going to stop. Even a van driver overtaking the bus might not have anticipated and/or seen you. In this case it looks like you were able to stop if necessary (just about!) although only because the driver was completely alert. But really I guess the point is that the pedestrian should have been a little more cautious, and perhaps the driver a tiny bit more so too. I'm sure the pedestrian didn't consciously think "ah, and emergency vehicle, it's OK it will stop" (although sometimes it is hard to tell where exactly the sirens are coming from... in which case a pedestrian might reasonably have "proceeded with caution and been prepared to stop"...)