Strange that the cycle lane goes through the pinch point , I have not seen that before , I have seen pinch points being erected and the white line for the cycle lane removed for about 10 metres either side of it so thought if there is a pinch point then you cant have the cycle lane as it obviously dangerous ..
Stick to the cycle lane there and you will have a very close pass.
Whether it is right or wrong we all know that many or perhaps most think it is fine to pass a cyclist as long as they are in a cycle lane. Magic white paint provides impenetrable protection. If the cycle lane isn't wide enough then don't cycle in it. I tend to ride on the white line itself unless it is wet or very narrow which discourages close passes whilst also minimising the "you should be in the cycle lane" crap.
As for Sainsburys it is a rubbish gig for drivers, lots of short journeys and you have to help unload each end. So it tends to attract the very worst agency drivers. There is a reason most of their lorries aren't branded.