The crane is reportedly 770ft and is only about 50m south of the river just where it bends from north-south to east-west. If, to conjecture, you're approaching from the north along the river and miss the bend in the fog you haven't got a lot of room left even at 800ft.
From the pictures, the flames on the ground are in Wandsworth Road, about 200m due south of the crane. So this does sound plausible.