That the Air Ministry didn't instigate a single-seater is always blamed on the navy, but it wanted them. There was definitely a disconnect between operational experience and what was being decided in the Air Ministry for the FAA in the 1930s, but there was a reason for it. Carrier deck space was limited and in the early 30s, fearing a size and weight increase in modern aircraft decisions were made that meant that dual role aircraft were gonna be incorporated on carriers, so the likes of the Skua and Fulmar were ordered. The other issue was cost versus predicting where the next threat might come from, the former being an ever-present issue in peacetime and the latter in that the British didn't anticipate the Germans would invade Europe again so soon after the Great War. Even before the Skua entered service it was criticised by senior admirals as being inadequate for their needs. The Hurricane was of interest and by the mid-1930s was being discussed as a future carrier single-seat fighter.
It would have been interesting to see the changes in RN and FAA procurement and ops planning had the Japanese carrier fleet been seen as a strong threat. Here's what's building in the UK and Japan through to end 1938, the end of which when Japan is invading China and US and British sanctions are beginning to bite.
HMS Illustrious, laid down Apr 1937
HMS Victorious, laid down May 1937
HMS Formidable, laid down Jun 1937
HMS Indomitable, laid down Nov 1937
HMS Ark Royal, commissioned Dec 1938
IJNS Hiryu, launched Nov 1937
IJNS Shokaku, laid down Dec 1937
IJNS Soryu, commissioned Dec 1937
IJNS Zuikaku, laid down May 1938
IJNS Akagi, reconstruction and comm Aug 1938
Clearly there was something afoot in the PTO that Britain could have paid some attention to, for example, what fighters and strike aircraft is the IJNAS using in this period. Had Britain considered that in addition to facing German and possibly Italian strikes, that it may need to fight the IJN's carrier forces at sea, the FAA, RN and AM might have made different decisions on aircraft.