In World War II, it was in hindsight a poor decision for the Royal Navy to stick with coal and an expectation of nearby friendly ports to refuel. The USN having oil-burning ships that could be more easily refuelled at sea meant an increased range and this made a difference in the pacific with most formerly friendly ports in the hands of the enemy. The Royal Navy may have been less happy with oil than coal due to not having a source on the British mainland.

Today, it seems unlikely that a Royal Navy aircraft carrier will be far from friendly ports. More likely for it to be used to launch air attacks against a relatively weak adversary (think of something like the military actions near the Arabian peninsula in the last 50 years or so). There are also Royal Navy oilers and other logistics ships that can replenish fuel or other resources.

Its fuelled with diesel, not natural gas. And all carriers need refuel at some point for their embarked aircraft.