Prison tower / St. Barbara's Church, Stonecutter's Island [????- ]
I think I've got the right location, based on the GeoInfo map, but let me know if it needs moving.
It's the last remnant of the short-lived prison that was built on Stonecutters Island in the 19th Century.
At some later date it became the Garrison church. I wonder what it is used for now?
There's a good photo from 1996 on Flickr. Sharing is restricted for this photo, but here is the link: https://www.flickr.com/photos/89154377@N02/9572513857/in/set-72157634364767445
There's also a painting of the tower from c.1984 on the BBC website: http://www.bbc.co.uk/arts/yourpaintings/paintings/st-barbaras-church-sto...