I've got one the same! From my grandfather who fought in France in WW1. He was Welsh. I have discovered that today's Royal-Welsh was back in 1916, the 38th (Welsh) Infantry Division which contained the Royal Welch Fusiliers, the South Wales Borderers and the Welch Regiment. They fought in the Battle of the Somme and at Mametz Wood. My grandfather told me (decades ago!) that he was at Arras 'Hindenburg Line', Bourlon Wood, Cambrai and then Bonn (Golsheim). I can't find any trace of him in wartime records though. As for the badge, it's still a mystery as I can't trace the Old Comrades Assoc.