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
Queer Heritage
An appellation used on plaques erected by Sexual Avengers commemorating sites of gay events/interest.
Jewish American Society for Historic Preservation
From their website: "The Jewish American Society for Historic Preservation is a non-profit, volunteer organization. The purpose of the Society is to identify and recognize sites of American Jewish ...
Heath & (Old) Hampstead Society / Hampstead Plaque Fund
The Hampstead Plaque fund was set up, many years ago, by Ralph Wade and has been administered by the Society ever since.
The Keskidee
Britain's first black arts and cultural centre. Named for a Caribbean singing bird (which seems to sing Qu'est-ce qu'-il dit?), it was founded by Oscar Abrams (1937-96). It had a library, gallery, ...
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