That's correct 4gs, the emphasis here is in the wording, once the pedestrian is on the crossing,,ie if the pedestrian is stood on the pavement, then he/she has no right of way.
I'm quite sure that at some time or other you have stopped for someone at a crossing only to find they didn't want to cross anyway.
Another point worth remembering is that when a pedestrian has walked past the front of your car, at a crossing, he/she has every right to turn and go back, so it is as well to make sure this doesn't happen.