Were the Hawkins cruisers a response to rumored German guns?

Did rumors of seven-inch German cruisers cause Britain to create the Hawkins class?

No; the terminology is anachronistic and a mere half-inch caliber advantage would not explain the British design choice.

The Hawkins class was not a simple response to rumored German seven-inch guns, and 'heavy cruiser' is anachronistic for the First World War. British naval intelligence had developed deep access around German yards and construction, so vague rumors carried less weight than they might in a poorly observed program. A genuine caliber-response design would likely seek a decisive jump, such as 9.2-inch guns. Moving only from seven to 7.5 inches would not provide the kind of overwhelming advantage expected from a deliberate answer to a new German cruiser.