One of the most difficult evolutions in the postwar Royal Navy was the transition from the Type 12 Whitby, Rothesay and Leander frigates to a replacement design. It took nearly a decade for the first Type 22 to enter service after the final Leander's were built.
The change in emphasis of the RN's roles in the 1960s from blue sea to NATO area, coupled with the increase in size and cost of new weapon systems does much to explain this.
The Type 82 destroyer began life as a high end Leander type frigate carrying the CF299 Seadart area defence system. The time taken to develop the missile and its size meant that the final Seadart ships the Type 42s were destroyers and entered service in the 70s.
Originally, the general purpose and asw versions of designs to replace the Type12 were similar in size and appearance, though a bizarre high speed variant of Type 19 was examined.
After 1966 the RN selected the Type21 to replace some of its older frigates while development began of the Type 22 for the crucial NATO asw role.
Sorry not to be able do any drawings, but I thought younger visitors might appreciate a summary of an account which fills many pages in several books.