During the 1930s the RAF began insisting on aircraft that could do a thousand and one things, the TSR spec, fighter/dive bomber specs, the latter of which meant no single seat modern fighter as a result and this hampered the FAA and the admiralty to no end in the years ahead to the point where it played catch up throughout the war - thank heaven for the USA and Lend Lease!
The last one for example meant that it didn't get a 'modern' single seater until the Martlet in late 1940, and even then it was only intended as a stop gap until something better came along (they wanted Spitfires, and the Firebrand to not be a turd). Prior to these combo all singing all dancing machine requirements to save money, the FAA had single seat fighters, torpedo bombers, general reconnaissance types, catapult aircraft (yes, the Swordfish was often carried as a catapult aircraft aboard capital ships, as was the Fulmar, interestingly enough, it was designed as a catapult fighter after all) and so forth, so the change came with the new generation of aircraft, although multi role aircraft had appeared before, naturally.
Oh yes they did. The RN effectively invented the modern carrier as we know it and the concept of the CAG. HMS Furious was the first aircraft carrier with a flying off deck and landing deck, although this wasn't used in action, only during trials owing to a lack of a means of restraining an aircraft on landing. Arrestor hooks came after the end of the war. Furious carried out the first successful carrier launched air strike in history, Sopwith Camels attacking the German airship station at Tondern, although because of a lack of arresting mechanism the Camels had to ditch or land and the pilots make their own way back (hmmm - imagine that during the Pacific campaigns - eek). The first CAG was what was known as F Sqn, commanded by Sqn Cdr Edwin Dunning, the same fella who carried out the dicey landings aboard Furious' forward deck and lost his life doing so, and was equipped with Sopwith Pups, 1 1/2 Strutters and Camels and Beardmore WB.IIIs (a Pup converted with folding wings and floatation gear especially for service aboard carriers), as well as BE.2cs for ground based training.
There was also HMS Argus, the first flat top carrier, commissioned in 1918. It did nothing of note during the war, but the very first aircraft carrier based torpedo squadron was embarked, but not flown from the carrier, 185 Sqn RAF equipped with Sopwith Torpedoplanes. Argus was instrumental in pioneering arresting systems and countless Sopwith Pups were expended landing on her deck and crashing into safety barriers...