This mentions St Faith's circa 1937
St Faiths, 2 Myddleton Square, controlled by by the Holborn Deanery Association
http://www.rootschat.com/links/01qmp/This mentions St Faith's circa 1928
There are no institutions (in Holborn) for unmarried mothers, illegitimate children, homeless children in the Borough but St Faiths Home, Myddleton Square receives such mothers from the Holborn area.
http://www.rootschat.com/links/01qmp/And found this:
"St. Faith's Home ( 1919 ) , 2 Myddelton Square , Clerkenwell , E.C. Object . — Rescue and preventive work , especially in Holborn Deanery . Admission . - Application to Lady Superintendent . Payment expected where possible "
So this appears to indicate that St Faith's existed prior to being formally enveloped by the Holborn Deanery Association?
I found a google book dated 1900 which appeared to list various institions, charities, associations and so on, and St Faith's/2 Myddleton Square not found in it - but there was a St Faith Home at 259 Vauxhall Bridge Road (and that was also listed in a 1891 book)
Have you a time period you are trying to match to? Is it "St Faith's" that is your point of reference, or is it the Myddleton Square or Holborn or Magdalen Homes?
Cheers
AMBLY