I shall mostly ignore the actual dispute and just comment on the junction.
It has the markings you would expect for a footpath crossing a road, in which case HC rule 59 and subsequent appear to apply (1). This does require drivers not to run into people using the footway, however nothing allowing people on the footway to run into the side of cars. The equivalent advice for cyclists appears to be rule 62, and for drivers rule 170, the latter referring to giving way to pedestrians, but not cyclists.
The underlying issue is the marking of the junction, which does not take account of the existence of the cycle track, which logically does require a give way line marking along its course, because cycles go faster than people on foot, this being the purpose of a bicycle. As usual the local authority has filed the marking question under the too difficult box.
I believe the pedestrian priority arises from the underlying fact that pedestrians are traffic on the major road, and so have priority over minor road traffic, the qualification 'if they have started to cross', reflecting the basic rule in the highway code that anyone already using a piece of road has priority over anyone arriving later and wanting to use it.
I think there could be an argument that irrespective of the markings drivers should be aware that they are crossing a cycle track and allow for the greater speed of cyclists, including observation left and right.
There is a similar lack of markings on the Portway cycle track in Bristol, where it is crossed by an exit from a football ground, and the sightlines are much worse.
Personally I would have cycled up to the junction with considerable caution, the ambiguity from mssing markings is an obvious source of danger, and it is always prudent to prepare for what people might do, not what they should do.