Why an automatic 6-inch gun could displace the 5.25-inch caliber

If Britain had a working automatic 6-inch gun by 1957, would the 5.25-inch gun still be produced?

No. A 6-inch automatic able to meet the same target profiles would make the 5.25-inch gun unnecessary.

A Mark N5-level automatic 6-inch gun would combine a heavier projectile with a rate of fire normally associated with smaller weapons. Automation restores the handling qualities usually lost when shell weight increases. The decisive condition is whether the mounting can engage the same air and surface target profiles expected of the 5.25-inch system. If it can, the intermediate caliber no longer fills a distinct niche and is unlikely to continue into production.