No, Britain has not been self-sufficient in food since basically the late 18th century. By that point, it became clear to British policy-makers that not only would Britain no longer be an exporter of food, as it had been in much of the early modern period, they would have to import in years of poor harvests. In years of abundance Britain could mostly feed itself.

The situation was largely disrupted by the French Revolutionary and Napoleonic Wars, however, as imports were harder to come by and prices rose substantially. This actually led to some important pieces of legislation with long-term consequences, including the implementation of the Speenhamland System in 1798 and the passage of the Corn Laws in 1815. The Corn Laws were a series of duties on imported grain implemented at the conclusion of the wars in order to keep grain prices high, and to continue the period of prosperity for landowners. Britain's population growth, however, meant that the problem of short food worsened over time. This led to the period (retrospectively) called the "Hungry 40s," and the repeal of the Corn Laws in 1846: with their repeal, we get proper "Free Trade" in food for Britain.

At that point, in 1846, British farmers typically produced about 75% of the wheat that Britons consumed. By World War I, less than 70 years later, that figure had dropped to less than 20%. And, in addition to wheat, Britain imported massive quantities of preserved and refrigerated meat from the US, Argentina, and Australia; butter and other dairy products from New Zealand, and continental Europe; and an assortment of other products like tropical fruits. These added to Britain's prior dependence on the tropical world for its chemical stimulants like coffee, tea, chocolate, sugar, and tobacco (not a food, but useful to consider in the same category), as well as spices. This utter dependence on overseas farmers was obvious their enemies in both World Wars, as evidenced by the resources Germany put into submarines. Their principal goal was to disrupt the trade in food between Britain the rest of the world--especially North America--enough to force the UK to a negotiated peace. Convoys, the US and Royal Navy, rationing, and government support for intensive agriculture prevented this from happening both times. In 1947, the wartime support for agriculture (itself a fascinating story of top-down environmental management) was made permanent with subsidies for intensive agriculture. Britain abandoned the free market for its food supply, and has been much more capable of feeding itself since then.

Also, I should point out that Ireland was in no way part of a separate economic system in the 18th and 19th centuries. It has long served as a combination of captive market for British goods and a supplemental granary for British stomachs.