OK, then - here goes...
In the 1911 census, look at the William George LITTLE, age 24 (approx. birth year 1887) living in Fulham with wife Margaretta May and daughter Margaretta Maud. He's a Commercial Motor Driver for (I think it says) Gamage's, the big department store on Holborn Circus, so maybe a mail-order delivery man or similar.
William George LITTLE married Margretta [sic] May DELLAR (born 30 May 1879) in Brentford RD, Q3 1907.
Margaretta [sic] Maud was born in Fulham in Q1 1909.
This man has a WW1 pension record on Ancestry, indexed as William John LITTLE (search for Last Name Little and Regimental Number 097610). A couple of pages do say William John, but most have William George, and the next-of-kin info matches. It gives Margaretta Maud's DoB as 4 Feb 09, and reveals that there was also a son, Harry Edwin born 20 Oct 1907 - the missing child on the 1911 census, who can actually be found as Edwin LITTLE X [sic], staying with Margretta's widowed mother Mary DELLAR X [sic!] at the address given in the pension record as WG's "address on discharge".
So this WG was M2/097610 Private - rising to Serjeant - William G Little of the (Royal) Army Service Corps, who enlisted on 10/5/15 and was transferred to Z Class Army Reserve on 24/2/19. He seems to have spent quite a while in hospital with appendicitis, for which he received a pension, and another "personal" ailment... for which he didn't.

This man was born in Hackney (Shoreditch is part of Hackney borough, I think?) around the last week of March 1886, as he gave his age as 29 years and 41 days at his medical exam on 8 May 1915. His occupation in civilian life is Motor Fitter & Driver, and he served in various Motor Transport companies of the Army Service Corps.
When looking at the pension record, remember to go backwards as well as forwards from the page Ancestry thinks is the first! It takes you to Image 4524, but you need all the images from 4520 to 4542!!
Margretta May LITTLE nee DELLAR died in Uxbridge district in Q2 1956 - the very same quarter in which your WG married Eleanor BRITTLE.
I've even found a photo of Margretta and daughter ...
http://www.dellerfamily.com/p3176.htmCould this be your man???
Adrian