Where an autoloading 5.25-inch destroyer gun would fit

Would a reliable autoloading 5.25-inch gun make Britain arm future destroyers with it?

Not the treaty-era destroyers, but the larger Battle class could plausibly carry it.

Automatic loading and fuse setting would make the 5.25-inch weapon much more attractive as a dual-purpose gun. Its physical weight remains too high for the destroyers Britain was building under late-1930s treaty limits. Installing it would consume too much displacement and stability margin on those hulls. Once the larger Battle-class type appears, the ship has enough scale for the weapon to become a plausible main battery.