Right of way for a raised crossing?
The vehicular and cycle traffic has priority, since the crossing is not a zebra crossing and there are no traffic lights, which are the only situations in which the Highway Code talks about pedestrians having priority.

However, as you have noted, many people seem to be confused by the crossing, so you should be ready to stop in case a pedestrian does step into the roadway or cycle lane. Also, be alert to the possibility of motorists stopping and beckoning pedestrians to cross into your path and the possibility of a group of pedestrians blocking the cycle path because it was clear when they started to cross but now they're waiting for cars on the road.