"from memory London Specials like you to be at 800ft, over the river i.e. on the Heli Route."
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.