There is this entry in 1911 which, if not our couple, is most coincidental.
https://www.familysearch.org/ark:/61903/1:1:XW16-D6R
Alfred, though, is not married at that time.
No that this helps with Alfred
Do you think
Annie Pearson might be the illeg. daughter of Martha who married Benjamin Pearson
Annie GarsideBaptism 24 Dec 1876 Ancoats, St Andrew, Lancashire
Mother
Martha Garside1881 census Piece: 3986 Folio: 36 Page Number: 14
Benjamin J. Pearson 31
Martha Pearson 26
Annie Pearson 5 Manchester Marriage
28 Mar 1881 Ancoats, St Andrew, Lancashire
Martha Garside age 26 father Thomas
Spouse
Benjamin PearsonAnnie Pearson is with the family in 1901 age 25 Manchester her occ gentleman’s hat trimmer but she’s
not with them 1911
EDIT to add it looks as if Mary Alice PEARSON was Benjamin's sister
Mary Alice Pearson age 64 abode
54 Ostrich Lane PrestwichBurial 17 Feb 1912 Cheetham, St Luke
Mary Alice Pearson, spinster probate 22 Feb 1912 to
Benjamin Pearson engineer
Mary Alice Pearson Birth 23 Apr 1846
Baptism 31 Jul 1859 Manchester, St Mary, St Denys and St George
Father Benjamin Pearson, Mechanic Mother Mary abode Manchester
Also baptised on the same day
Benjamin born 11th July 1850Thomas born 3rd July 1852