According to the BFI database, Sidney G. Griffiths lived from 1899 to 1967. IMDB credits him as an actor in the 1903 short A Desperate Poaching Affray, but this obviously contradicts the BFI's chronology; the actor is probably a different Sid Griffiths.
Griffiths' first film, then, appears to have been 1925's Jerry the Troublesome Tyke, which he wrote, directed and animated. Jerry went on to star in 41 subsequent films as part of the Pathé Pictorial magazine, the last of them appearing in 1927. This was one of the longest British animated series in the era of theatrical animated shorts, and the first animated series to be made in Wales.
Jerry is a sort of hybrid of Felix the Cat and G.E. Studdy's Bonzo, but lacking either the iconically stripped-down design of Felix or the delicate rendering of Bonzo. He's actually a little disconcerting: from the neck down he looks like a swollen, naked human.
The Jerry cartoons, although reasonably good for their era, haven't aged as well as some of their contemporaries. What saves them is their general sense of playfulness: the first carton introduces us to Jerry's parents, an anthropomorphic pen and inkpot, while Griffiths is always on the lookout for new locales for his character to visit, often placing Jerry in front of like action backgrounds (In and Out of Wembley is a particularly good example of this). Even the shorts which are generally unremarkable tend to have a good sequence or two, such as the train ride in Honesty is the Best Policy.
My personal favourite is Ten Little Jerry Boys, which doesn't bother trying to tell a story and instead strings together a set of gag sequences. This seems to have been Griffiths' strong point.
After the Jerry cartoons, Griffiths appears to have worked on only a handful of films. In 1930 he, Brian White and A. Goodman co-directed Tropical Breezes, a short cartoon about two castaways. In 1933 he worked on two shorts written by the popular cartoonist H.M. Bateman: Colonel Capers (directed by Adrian Klein, animated by Griffiths and White) and On the Farm (Directed by Griffiths, White and Joe Noble).
In 1935 Griffiths began working as a supervisor at Anson Dyer's studio Anglia Films, beginning with Sam and his Musket and staying in this role until Gunner Sam in 1937. Griffiths does not appear to have worked with Dyer during the latter's stint at Publicity Films, but the two worked together again when Griffiths provided animation for You're Telling Me, A.G. Jackson's documentary about Dyer's studio
This would seem to have been Griffiths' last piece of animation. I can find only three more credits for him, all as a camera operator at Halas & Batchelor: Animal Farm (1954), The Candlemaker (1957) and Man in Silence (1964).