Looks like I may have been correct with Sydney's parents - here's his baptism in Stratton St Margaret...
13 Mar 1884 (born 14 Jun 1883) Sydney Charles Page son of William and Jane, Union Workhouse, lab
I was unable to find his parent's marriage in Liddington, Stratton St Margaret or Swindon Christ Church.
There was no marriage for Sydney in Stratton St Margaret in 1908.
Dave