Looking at those two Alfred Jones marriages, I have to say I think that the signatures are very similar.
Don't forget, re 1911 census signature, that he probably wrote out the whole form himself, so you have a good sample of his handwriting.
Did he ever use the David name again?
There are baptisms of children of Alfred and Annie Jones at St Luke Victoria Docks from around 1896. He appears to be just Alfred on those. Unfortunately - with the libraries being closed

- I can't get hold of the more detailed transcriptions.
Does Linda have the Alfred who married Annie in the 1901 census? Presumably they are in West Ham. Because I can't see him! Daughter Rebecca was born 1899 (21 May according to ancestry)and she should be easy to spot.
Here they are in the 1911 free index
https://www.familysearch.org/ark:/61903/1:1:XWF3-WFMAlfred's details are a pretty exact match for the earlier records. Wife Annie is born Camden Town, they have a 14 year old son James, then Rebecca, 11, Rose, age 9, and two younger children.
According to the ancestry transcript of the St Luke's baptism record, Rose was Rose Alice, and was born 28 Nov 1900. Baptized in October 1901.
But can that be right?

Birth reg in Dec 1901, fitting with age in 1911
JONES, ROSE ALICE
Mother's Maiden Surname: JONES
GRO Reference: 1901 D Quarter in WEST HAM Volume 04A Page 161
Looking again in 1901 in West Ham, there is a family in the same street as Alfred and Annie were in 1911, and with
some similarities, but plenty of differences!
piece 1580 folio 170 page 45
54 Devonshire Road
Just to confuse, first household is William Jones, 40, Dock Labourer, and wife Amy
Second household
Arthur Jones Head 32 Stevedore's Labourer, born London St Georges
Annie Jones Wife 32, London Camben Town (looks like)
John Jones Son 4 Essex West Ham
Rose Jones Daughter 1 Essex West Ham
Walter Preston Boarder 23
Trabscript here
https://www.familysearch.org/ark:/61903/1:1:X9NC-GC2So Mr Jones has a different first name. but the rest is the same.
Annie Jones pretty much matches the 1911 details.
Children's ages correct, names wrong, but Alfred and Annie were soon to have a daughter Rose!
Can this couple be eliminated?

Has anybody got more info from the baptisms at St Lukes?
John