A Bleach Works was where fabrics (cotton, linen, wool etc) were bleached, not where bleach was made. Fabrics were repeatedly soaked in natural alkaline solutions (like ash and water) or stale urine (for wool) to remove greases and impurities. The wet fabric was then laid out for months on open grass fields (called crofts) to be whitened by the sun and air, these were known as Bleachfields.
See Blackrod Bleachworks and Wallsuches.