Royal Navy automation before the G3 era

Did the Royal Navy begin investigating ship automation after the G3 design?

No; mechanization work dated to the 1880s, and the long-running efficient-ship effort predated G3 by decades.

The Royal Navy had pursued machinery, mechanical assistance, and reduced manual workload for decades before G3. With prewar technology, much of the practical gain would come from redundant and alternate systems that reduced maintenance demands rather than from eliminating every operator.