This very old application was approved but obviously never built:
I can’t see a more recent application in this area.
Interestingly I have a paper map which was handed out at the start of the scheme, showing not only the 300 which started off the scheme but also the proposed 100 next ones. It wasn’t a great success as a lot were never built, including the one you mention which on this map appears right outside the Florence Nightingale Museum. It would certainly be useful to have one there. Another location in that area which never happened was Portcullis House.