I've had a look through registrations and found some information, but I don't know how much of this you already have.
Firstly, it seems that your Sydney always appears in records as Sidney George Smith. his death registration is:
Name: Sidney G Smith
Birth Date: abt 1882
Date of Registration: Mar 1922
Age at Death: 40
Registration district: Woolwich
Inferred County: London
Volume: 1d
Page: 1843
Ethel's is:
First name(s) ETHEL L J
Last name SMITH -
Birth year 1892
Age 30
Death quarter 1
Death year 1922
District Woolwich
County London
Volume 1D
Page 1846
It seems odd that they died so close together, and both at a relatively young age.
I found Ethel's birth registration:
Name: Ethel Louisa J Berry
Registration Year: 1892
Registration Quarter: Jan-Feb-Mar
Registration district: Camberwell
Volume: 1d
Page: 901
I couldn't find Sidney's as Sidney Smith is a common name, but I suggest get their marriage certificate, as this will show their fathers' names, and should allow them to be found on the census to give their place of birth. The marriage details are:
Name: Ethel Louisa J Berry
Registration Year: 1910
Registration Quarter: Apr-May-Jun
Registration district: St Marylebone
Inferred County: London
Volume: 1a
Page: 1117
Records on Page:
Name
Laura Frances Barnes
Ethel Louisa J Berry
William Henry Holland
Sydney George Smith
(on that one he was Sydney).
You can order a certificate on lie from
https://www.gro.gov.uk/gro/content/
I think the current price is about £9.50 for UK, not sure how much for overseas.
I hope this is of some help to you.