Why light cruisers did not need to jump to 15,000 tons

Would Britain build 15,000-ton six-inch light cruisers after the Emerald class?

Probably not without an operational need; light cruisers were meant to provide useful numbers and a supportable overseas presence.

A 15,000-ton light cruiser is rejected unless the navy needs the capability that requires that size. The Town class had reached roughly 10,000 tons by the late 1930s, but that does not justify making the same jump immediately after Emerald. Light cruisers were meant to be available in useful numbers, move quickly, and maintain a presence around the world. Ease of supporting them overseas also mattered. Twin six-inch turrets alone would not explain the proposed increase in displacement.