|I see that an Ethel Louisa J Berry married in Marylebone London during the period April to June 1910 under the GRO reference, 1a, 1117 and one of the possible partners was a Sydney George Smith, so presumably this is your Sydney Smith.|
Looking for them on the 1911 census, I can only see one Sydney and Ethel Smith who have been married under a year and that is a couple living at 19 Protheroe Street, Fernlea, Glamorgan in South Wales a long way from London or Woolwich which makes it rather doubtful that they are your couple. However this Sydney Smith (no other names or initials given was age 29 which seems correct and he gives Dartford Kent as place of birth which show there is a connection close to Woolwich. Edith is age 25 and gives Alverstoke Hants. as PoB, as you presumably have information on her, then if she fits there is a good chance that they may be correct.
I cannot see any births in Dartford around the early 1880s for either a Sydney (or Sidney) George or Daniel Smith, however there are some registered just Sydney (or Sidney) in Dartford or nearby. Second or further names are often added at baptism or later so any could be the one that you are looking for, there is one Sidney George Smith in the West Ashford district in Dec. 1882,but that is many miles from Dartford. There are also a number of possibles on the 1891 and 1901 census.
I suggest that you purchase a copy of the marriage certificate which should give Sydney's father's name and occupation, providing he knew his father, which may assist in spotting him on an earlier census, enabling you to narrow the search.