Why the Fleet Air Arm moved beyond a dedicated dive bomber

Did the Battle of Britain turn Britain against dive bombers?

No. Britain retained dive-bombing capability but preferred rockets and other systems over a dedicated dive-bomber force.

The Battle of Britain did not cause Britain to abandon dive bombing as a technique. Aircraft retained the ability to make diving attacks even though the services did not preserve a dedicated dive-bomber category. Rockets and other weapons offered flexible ways to support naval and land operations without maintaining a single-purpose type. The shift therefore reflects a preference for different delivery systems, not a conclusion that steep attack profiles had no value.