The founders included Edward Garnett, G. K. Chesterton and Conal O'Riordan.
It was just one of a number of similar London groups (Garnett had another Soho circle that was distinct); it was perhaps the most substantial such grouping of its time, with a concentration of those enjoying professional success.
The name was for Mr. Square, the philosopher character in Henry Fielding's Tom Jones.
Others who participated included J. D. Beresford, Walter de la Mare, John Galsworthy, W. H. Hudson, Roger Ingpen, Edgar Jepson, Arthur Machen, John Masefield, and Edward Thomas.
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