Hello Grace, I am a grand-daughter of Marjorie Edith Wood. I have been doing a bit of searching as well. I have William Wood living in London in 1901 census with Samuel Withers and his wife Elizabeth, who I believe is Williams daughter. I think she is Samuels second wife and don't think they had children of their own, just Samuels kids from first marriage.
I also have a copy of Edgar Isaac Woods birth certificate, he died 04 June 1913 at Dartmouth Cottage Hospital, Annie is listed as his widow. Not sure if Carol knows this, we certainly didn't.
I also have a copy of a death certificate for a Edgar William Joseph Wood, who died 25 Feb 1974, at the Rochford General Hospital, Essex, dob is 04 Oct 1898, Devon, can't decipher the place of birth but it is not Horrabridge, but sometimes people don't know where they were born!His occupation is retired heating engineer,however everything else matches so feel it could be the son of Edgar and Annie.
I enjoyed reading the letters sent from Billy, made me wonder if Ethel may have lived with Annie and Charles Wood in London.
Regarding Edgar WJ Wood, I think it is possible that he went to war, if he was born in 1898, he could have gone to war in 1915/16 onwards.
Happy to send copies of anything to you, let me know,