This is a woven silk formation badge representing the Coast Artillery Training School that would have been worn on soldiers battledress during the Second World War. I believe the badge was made by Brough, Nicholson & Hall.
At the start of the war the Coast Artillery Training School was located at Shoeburyness in Essex, but with the threat of aerial attack growing they relocated to Great Orme's Head outside Llandudno in North Wales in September 1940.