I had a similar situation, probably 10 years ago, but I was the pushchair-pusher. It still makes me cross to think about it. In your situation, as you describe it, my opinion is you were both wrong. You saw the pedestrian who was clearly intending to cross the road and you did not slow down and wait, and equally the pedestrian (who was probably aware of your vehicle,) went ahead to cross the road without due care and attention. Both of you should have stopped and looked, and neither of you had full right of way.
In my case the female driver shouted out of her car that she had seen me and had to slow down. The irony of this only struck me later when I thought "yes, you saw me, and yes you had to slow down". My situation was slightly different in that I was definitely well ahead of the vehicle and had commenced crossing prior to the vehicle reaching the left-turning. The driver clearly felt it was her right of way to turn left into a smaller road without having to worry about pedestrians.
As you have exhibited in your post, vehicle-users do generally seem to feel they have the right of way, and practically-speaking usually get it as they are more likely to cause damage to a pedestrian than the other way around.
Perhaps also note the first bullet of item 170 in the Highway Code which reads:
"Take extra care at junctions. You should
- [font]watch out for cyclists, motorcyclists, powered wheelchairs/mobility scooters and pedestrians as they are not always easy to see. Be aware that they may not have seen or heard you if you are approaching from behind"...[/font]
Meaning it's everyone's responsibility to be aware of potential hazards, regardless of who has the right of way.