You’ll note the Sun is not visible through the tip of the Shard, from the south side of St Olaf House. And as I suspected on my chance passing on 17th April, the shadow had long left the river. This was taken at 12:56:
No tip visible on the river, and no Sun visible through its prongs. The shadow must fall between these two points, on the roof of St Olaf’s House. So unseen I pinned it to the map there.
Shard Analemma 