On looking further at this on LIBINDX, I see that Edgar Watson's mother was Helen Taylor Edgar, daughter of James Edgar and Isabella Ingram.
Helen's sister Beatrice Gordon Edgar (1883-1971) married my second cousin twice removed, James Stephen Souter, in 1913. There were three daughters and one of the daughters had three of a family.
The birth date for Edgar Watson will have been arrived at by subratcting his age according to the gravestone in Aberlour from the year of his death, so if his birthday was later in the year than the day of his death, it will show as a year later.
From the indexes to births there were at least three children of George Gray Watson and Helen Taylor Edgar
Beatrice Isabella, birth registered Lewisham, 1898, December quarter
Edgar, birth registered Edmonton, 1900, September quarter
Vera Mary, birth registered Edmonton, 1903, September quarter: LIBINDX says that she died at Craigellachie Hotel on 8 January 1909, and there is a matching listing on SP.
There are other Watson/Edgar children born in Chester-le-Street after 1913, but they are the family of Peter Watson and Elizabeth Edgar and have nothing to do with George Gray Watson and Helen Taylor Edgar.
So it looks as if someone has confused Edgar's mother's name with his sister's.
I also wonder if Edith Larkin is Edith Tucker or Watson, wife of Edgar Watson and not of Edgar Larkin.
I see that George Gray Watson was twice married, his first wife being Elizabeth (Bessie) Glen Garden, whom hae married in 1887. There were two sons
George Glen Watson, birth registered West Ham, 1890, September quarter
Douglas Garden Watson, birth registered West Ham, 1891, September quarter
Bessie died in 1891, death registered in West Ham, 1891, September quarter. LBINDX gives the date of death as 9 September 1891, so she must have died very soon after Duglas' birth. She is buried in New Elgin with her parents, brother and sister. I see that a Douglas G Watson, aged 9, died in Elgin in 1901. Could this be him?
I have failed, so far, to find any of the family in the 1901 of 1911 census in Scotland or in England and Wales.