Looking at the track of the last bit of the flight before the collision, the turn over the Thames from westerly to easterly heading was made to the right, presumably because the pilot is in the right hand seat and it feels more natural to turn that way (??). The second turn back onto a westerly heading was also to the right, and the natural place to look is into the turn, so the building and crane would have passed across the pilot's line of sight quite rapidly. What was the back-drop behind the crane from that point of view? London is a bowl, so there is rising ground to the south of the river.
There were 7 seconds elapsed and about 125m travelled between the Battersea frequency change being acknowleged and the collision with the crane. Given that the frequency was not one anticipated, perhaps this required it to be set on one radio rather than a simple selection of a pre-tuned radio.
A very short time, an obstruction subtending a narrow angle with potentially an urban back-drop, an in-cockpit task...