Britain already had 9.2-inch cruiser ideas after World War I

Would Britain wait until the mid-1920s to begin work on a 10,000- to 15,000-ton cruiser with 9.2-inch guns?

No; such ideas existed after World War I, but Britain initially favored more numerous 7.5-inch commerce-protection cruisers for the threat it expected.

British designers did not need to wait until the mid-1920s to imagine a 9.2-inch cruiser. Relevant ideas already existed at the end of World War I. The Royal Navy chose a 7.5-inch route for ships expected to cover broad areas against disguised merchant raiders, where numbers mattered. A purpose-built heavy raider analogous to the later Deutschland class would demand the greater striking power of a 9.2-inch ship. The expected raider threat determined the chosen caliber.