The only reference we could find to this society was on the website of the  which has some documents in its 'Environics Collection' which is about how St Mary the Virgin Aldermanbury was moved to Fulton, Missouri.  So we guess the society is (was, probably) an American-British Friendship group set up after WW2 and that the Charing Cross plaque was erected then.
This section lists the memorials created by the subject on this page:
Angle-kin Society
Creations i
Charing Cross Station - US President
The Guardian has a detailed description of the procession from Charing Cross ...
Other Subjects
William Silver Frith
Sculptor. William Silver Frith. Born Leicester. Other London work: Metropolitan Life Assurance Company building in Moorgate; Imperial College, South Kensington; Two Temple Place. William Silver Fr...
3 memorials
1805 Club
Founded to preserve monuments and memorials relating to Lord Horatio Nelson and seafarers of the Georgian era, and to promote research into the Royal Navy of the Georgian period.
1 memorial
Vernon Hall
It occupied the building that once was Bow Public Library. We can find find no further information about its function, nor who Vernon was.
2 memorials
Circus Friends Association
Founded, as the Circus Fans' Association, in 1934 at Olympia, with the 'involvement and encouragement of Bertram Mills' Circus, to 'champion the cause of the circus in England, to right injustice, ...
1 memorial
English and American Browning Society
Plenty of Browning Societies exist, but we can't find one with this specific name.
1 memorial
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