The father Edmund John Waghorn (40 in 1891) may have died as Edward Waghorn, 49, in Greenwich, Sep qtr 1899.
it may be that he used the names Edmund Stephen at certain points, or at least that family members used those names of him - certainly on the delayed (10 Apr 1906) Greenwich baptism of daughter Jane Caroline Waghorn, born 1891*, her parents are listed as Edmund Stephen (deceased) and Maria Jane, of 51 Hardy Cottages.
*The register is endorsed with a birthdate of 30 Oct 1901, but this is clearly a decade out; Jane was 9 in 1901 and birth reg was Dec qtr 1891 Greenwich.