I have unfortunately no information about the origin of this brooch, but it looks to be the same brooch as the one worn by Princess Anne for the Easter service in 2009. It looks like a golden Celtic cross.
Easter service 2015:
Princess Anne, Princess Royal leaves the Easter Sunday service at St George's Chapel at Windsor Castle on April 5, 2015 in Windsor, England. (Source: WPA Pool/Getty Images Europe)
Easter service 2009:
Princess Anne attends an Easter church service at Windsor castle on April 12, 2009 in Windsor, England. (Photo by Arthur Edwards/WPA Pool/Getty Images)