I think the best British Naval fighter used during the war was the Fairey Firefly
http://www.fleetairarmarchive.net/Aircraft/firefly_wb271_preserved_flying_RNHF.jpg
First flew on December 22nd 1941 (soon after Pearl Harbour was bombed) and was a two-seater naval fighter - it was built under the understanding that (in the Royal Navys opinion at the time) all Navy fighters should have a navigator onboard to navigate for the pilot while at sea (several incidents of pilots becoming disorientated and lost while flying bombing missions and long-range partols in bad weather in combat conditions led to this decision) so the Firefly was no different.
The Firefly became fully operational in October 1943 on board the carrier HMS Indefatigable (the aircraft carrier my grandfather served on was the HMS Implacable - the Indefatigables sister ship) and escorted bombers during their attacks (most notably against the Tirpitz in 1944)
The fireflys were often used to 'scout ahead' to claer enemy fighters from the area before the bombers came through
It was used as a nightfighter in 1943 and often intercepted V1s and Heinkel He111s during raids
whilst stationed in the Pacific in 1945 Fireflys took part in the destruction of an Oil refinery in Sumutra - they had a tremendous operation record whilst fighting in the Pacific proving to be a versatile opponent for the Japanese - operating both day and night as a recon plane or fighter bomber
In June 1945 Fireflies of 1771 Squadron, operating from HMS Implacable, took part in attacks in the Carolinas, while in July 1772 squadron aircraft, from HMS Indefatigable, were flying strikes against shipping and ground targets in the Japanese home islands, becoming the first FAA aircraft to fly over the Japanese mainland. On 24 July, 1945 aircraft from 1772 Squadron became the first British aircraft to fly over Tokyo
They were also used to drop supplies to prisoners of war during these historic trips over Tokyo
It performed well in dogfights despite the Firefly's size and was armed with four 20mm cannons as well as rockets and mines (for the bomber role)
These are its stats:
Speed: 316mph
Ceiling: 28,000ft
Range: 1300miles
Wingspan: 44ft
Length: 37ft 7in
Weight: 14,020lb
It was so successful as a Naval fighter that it continued to be used on Royal Navy carriers during the Korean war
I think this plane was the best naval plane designed by Britain solely for use on carriers (i.e the American planes such as Hellcats and Corsairs don't count!
)