Why Royal Navy air-defense ships become destroyers

Why did the anti-aircraft frigate idea not work out for the Royal Navy?

Britain's radar and missile requirements demanded a destroyer-sized ship, unlike the smaller frigate sought by its Horizon partners.

The Royal Navy wanted a larger hull with taller masts, longer radar horizon, and more missiles than a conventional frigate could provide. In the Horizon program, Britain effectively wanted a destroyer called a frigate, while France and Italy wanted a genuine frigate. Those different operational aims produced requirements that were technically negotiable but institutionally difficult to reconcile.