Hi there, and welcome to Rootschat!
Ancestry might be more worthwhile at attracting descendants if you got a few more surnames (as in, William's aunts married names in there).
William Sr. had a lot of siblings, so the girls may very well be with family, but blacked out still.
They may have gone to the grandparents first, but it looks like Annie died 1938, and George died 1939. I got this by searching for a possible marriage of Caroline (William Sr's youngest sister).
That led to her being married to a Peter Carmichael. Looking at them on the 1939 led to the finding of brother George Egglestone living next door (George is on the 1891 census with the rest of them). And this led to:
Newcastle Evening Chronicle 03 February 1939
Egglestone.--Jarrow, 1, Pitt Street (the resi-
dence of his son-in-law, Peter Carmichael), 1st
inst., George Thomas, dearly beloved husband of
the late Annie Egglestone. Interment Saturday,
leaving residence 3 p.m.
Anyways, if you can dig up a few more names to add to your tree to attract more people, and hopefully also find trees for the married names, it might give you people to contact.
Edit: William Sr's sister Emley (Emily) appears to have married Mathew O'Neill . (GRO confirms the mmn for their children showing on the 1939)
2nd Edit: William Sr's sister Annie married Charles McCrudden, per George's military records. George and brother Harry were both in the Durham Light Infantry. There are records for a James Adamson of Chester Le Street for the Durham Light Infantry, although I think they are all in different battalions.... just looking for some link between the families!