Why the Royal Navy preferred more light cruisers

Did the Royal Navy plan to convert County-class heavy cruisers after deciding it preferred light cruisers?

No. It preferred new six-inch cruisers because they delivered more hulls and high fire volume within treaty tonnage limits.

The preference concerned fleet numbers, not conversion of existing County-class heavy cruisers. Six-inch armament allowed smaller turrets and hulls, producing more ships within treaty tonnage limits while retaining a strong rate of fire. The later Town class showed that Britain could also build a large cruiser around light-cruiser guns when it wanted greater overall capability.