I think it's almost entirely the cyclist at fault. His lane is blocked, so rather than pull out properly, he tries to squeeze through in the door zone and then rather than merging into the traffic flow he hangs off the inside of the car. When the cycle lane ends, hes still hanging off the car all the way accross the junction and still keeps to its inside when the lane narrows and is unsurprisingly squeezed. It's hard to tell from the camera angles, but as the car drives off, it looks like it was pretty close to the center line, which the car in the outside lane was also very close to, so giving as much space as he realistically could. I don't even see it as a failed overtake, the cyclist was joining the road from the cyclelane into traffic.
Unless the cyclist is a dwarf, his view of the road ahead would have been much higher and clearer than the video looks too, he'd have had loads of time to see that him and the 4x4 werent going to fit very well into that approaching gap, its ridiculous that he doesn't back out of that position until the car (nearly?) touches him.