This really is a mystery! Like the others, I can't find any Eileen Winifred Haydon or similar about the right time. Hadens is well-known Walsall legal firm, but this may be irrelevant.
I have found some records that may help.
Death of James Haydon 1925 Jan-Mar Walsall 6b 877 age 80. There appears to be no probate calendar entry to fit. Birth about 1845 doesn't seem to lead to a spouse named Gertrude, Florence or permutation.
Death of Florence Haydon 1936 Oct-Dec Walsall 6b 672 age 75 (born about 1861). At least she was of similar age. Probate calendar says Florence was a widow, date of death 17 Dec 1936, with administration to William Frank Haden. Estate £1,093 11s 6d.
Birth William F Haden 1815 Jan-Mar Walsall 6b 1356, mother's maiden name Goodchild. However, I can't find any Haydon or similar connected to Goodchild or similar. I can't find a marriage of a Gertrude, Florence or similar to a Hayden or similar or a birth of Goodchild with the right names.
Census 1911. Gertrude Florence Haydon age 24, married 1 year or less, military, but no place. Birth about 1887 Leeds, Yorkshire. Clearly, someone named Gertrude Florence married a man named Haydon in about 1910-11, and there are some candidates, bot none named James. Given the birthdate this seems unlikely to be the Florence Haydon above.
Regrettably, I can't find anything to connect any of these people, but maybe someone out there can get a bit further.
It looks like getting the entries of death for James and Florence is the place to start. The locations and informants might help to connect them.