Why the E-class did not receive a new main battery

Did the Royal Navy try to rebuild E-class destroyers with a modern dual-purpose main battery?

Not as a general programme; the ships were still new, and their existing 4.7-inch guns had originally been regarded as dual-purpose.

The E-class was still relatively new and did not appear to require wholesale rearmament. The A through E classes dated from the late 1920s and early 1930s. Their 4.7-inch battery had been considered dual-purpose when designed, even though wartime air threats exposed its limitations. No urgent programme replaced the main guns across an otherwise modern destroyer class.