Another passenger list
9th October1937
All three travelling on the Orcades, from London to Sydney Australia (intending to remain there)
Previously at 116 whirlowdale road, Sheffield
Added:
Quite a few voyages to and from Melbourne, and tourist trip to New York.
Still not totally convinced it is the right family but it would explain why no obvious birth or marriage record in uk.
And why do they keep returning to Sheffield, and then why Taunton 

They may have married in Sarawak
On one the passenger lists I saw gives birth place of
Edward Charles born London,
Doris May born Sheffield &
Edward Ross born
N(M?)iri, SarawakCalifornia, San Francisco Passenger Lists, 1893-1953added for info.
Sarawak births and deaths
1921 - 1923 are held The National Archives, Kew
https://discovery.nationalarchives.gov.uk/details/r/C6529734 this is available to download from The Genealogist. Partner websites are free to search but there may be a charge to view full transcriptions and download documents
On 1939 Register in Somerset Taunton there is
Edward C b1893, Doris M b1892 & Edward R Thornton b1922
Edit to add
The
1947 probate record Administration Wakefield for
Edward Ross Taunton died 5 Mar 1945, father
Edward Charles Thornton,
Hotel Proprietoraddress
Winchester Hotel Castle Green Taunton matches address 1939 register