The green crossing strip connects the two sides of the shared cycle/pedestrian pavement on either side of the road where there is a shared drop-kerb. The road users approaching the green cycle/pedestrian crossing from either side have to give way to anyone using the green crossing point, ie the van driver has a give way dotted line and you, on the road approaching the green crossing point, have a give way dotted line. Both you and the van driver have to give way [ie stop] if there is a pedestrian or a cycle on the pavement crossing point.
What the green crossing point does NOT do is give a cyclist, on the road marked cycle lane, the right to turn right from the road onto the green crossing. That is the equivalent of approaching a zebra crossing or a pelican crossing and then turning right off the road in front of traffic onto the opposite pavement and expecting any traffic coming from the opposite direction to stop for you because you are then on the crossing..
The only direction a cyclist using the road cycle lane should follow is the indicated cycle lane straight on over the green crossing, stopping to give way if anyone is using the crossing. It does NOT give anyone using the road the right to turn right off the road cycle lane at that point, as shown on the still where you can clearly see the straight on arrow marked on the road marked cycle lane - if the road cycle lane users had the right to turn right in front of approaching traffic at the green crossing point there would be an arrow also pointing to the right on the marked straight-ahead arrow.
However, if there is nothing coming and no-one is adversely affected then who would be bothered if you do turn right there?
Just don't blame the van driver for not stopping or giving way to you in this instance.
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That's an excellent analysis.