Still not finding John William in 1911, though I am intrigued as his service entry in the Tank Regiment in 1927 gives his mother as his next of kin. Did your Grandad, ever talk to your Dad or other family members about his early years? Perhaps he was only temporarily separated from his mother, maybe while she was a patient in the workhouse in Elswick in 1911?
https://www.familysearch.org/ark:/61903/1:1:XWMH-L52Doesn't explain why I can't pinpoint him in 1911, though.
From what I can see in the records Mary Beatrice was the child of William Thorpe, a book binder and his wife Mary
Born 21 Aug 1888, Baptised 26 Sept 1888 at St James, Gateshead
https://www.familysearch.org/ark:/61903/1:1:N2YQ-778Her birth (according to the GRO site which gives mother's maiden name prior to 1911) was registered in Gateshead Q3 1888, mother's maiden name Bowman
She married Henry Alfred (Harry) Harwood in Q3 1912 - as Girl Guide has posted.
Two possible children of this marriage Doris S, born 1913, Newcastle and Harry I, born 1915, Gateshead
Her husband died in 1959
Newcastle Evening Chronicle 30 Nov 1959, page 15 col 2
HARWOOD Gateshead 45 Milling Street in hospital on Nov 26 aged 77 years Henry Alfred dearly loved husband of Mary Beatrice, Interment Saltwell Cemetery on Tuesday 3.15 pm. leaving residence 2.45 pm. Funeral private.Saltwell Cemetery Index entry shows he was buried in Division 4 Grave 4417 on 1st December 1959.
https://www.familysearch.org/ark:/61903/3:1:3QSQ-G96W-KS68?i=92&cat=825084Mary Beatrice died in 1966
Newcastle Evening Chronicle 18 Feb 1966, page 4, col 2
HARWOOD Gateshead late of Millington Street, Feb 14 aged 77 years, Mary Beatrice dearly loved wife of the late Henry Alfred. Was interred today Saltwell Cemetery.
Saltwell Cemetery index shows ahe was buried in Division 4, Grave 4548 on 18th Feb 1966
https://www.familysearch.org/ark:/61903/3:1:3QS7-996W-KSDH?i=95&cat=825084I'll have a look at Mary Beatrice's parents and siblings tomorrow, maybe he was with a relative in 1911, perhaps mistranscribed ?
Boo