The badge is a broken S in wreath as previous posters have noted.
The metal S in wreath was a skill-at-arms badge for qualified surveyors, flash-spotters and sound-rangers of artillery survey units RAA(M), and battery surveyors RAA or RAA(M), and was introduced in brass in 1931, becoming available for issue in 1932. It was worn on the left forearm only by those so qualified.
The blackened badge suggests post December 1939, skill-at-arms competitions ceased to be held in 1941.
Trade badges were worn on the right arm above chevrons, or on the right forearm below the badge of rank by warrant officers. These ceased to appear in War Scales of Clothing and Necessaries in 1942, and were not listed in various General Routine Orders of 1943, 1945 and 1947 listing badges of rank and appointment that were to be worn by other ranks.
It would be wholly implausible for a tinsmith or plumber to wear the S in wreath - the trade badge for a tinsmith and whitesmith, or a plumber and gasfitter, who qualified annually prior to the Second World War as an Artificer - Field Engineer RAE or RAE(M), was a grenade, "...similar to that mentioned in SOs for Dress 1935, para 290(c)...".
Keith
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