After having crippled the Luftwaffe over Southern England, could Britain still have been starved into submission by the German Navy/Airforce, or did they become self sufficient by this time? (In terms of food, mostly.)
Even before the war Britain actually only produced around a third of its food. The height of the Atlantic war was 1941 - 1942. Britain was heavily reliant on imports of food and clothing during this time, it was vital that these resources were received.
Whilst meat, butter, bacon, tea and sugar were all put on ration in the first half of 1940, in 1941 Jam, cheese and eggs were added to the list, alongside clothing and coal. Not only was coal needed for ships but actually mining it became harder as miners left to fight. The situation became so dire in 1943 that Ernst Bevin started his ballot scheme, instead of serving in the forces some conscripts found themselves doing their national service in the mines - a "Bevin boy" as they were known.
In 1942 dried fruit, rice and even tinned vegetables were added, the shortage of sugar caused chocolate and sweets to be added late 1942/early 1943. The amount of food that rations permitted was about half of the original by the start of 1943. After the war rationing briefly increased (bread rationing in 1946) but was slowly phased out and didn't finally end until 1954.
The government gave lots of advice on how best to make food rations go further - Woolton pie being a well known one. Some of them still stick with us today - I still hear of peopling having "bubble and squeak" for example. Advice and help was given with clothing too - patterns of re-using an old overcoat to make new garments, even tablecloths and the sort, there was the phrase "make do and mend" - encouraging people to re-use or repair old clothing. The Womens Land Army sought to replace workers on farms who had left to fight.
Despite all this Britain badly needed the imports from the USA, the war of the Atlantic was the only thing that really scared Churchill he later stated. The u-boat hunting grounds in the mid Atlantic, safe from air cover allowed the u-boats easy hunting - this area was known "the gap" where convoys and their escorts were on their own.
The work undertaken by GC&CS at Bletchley park was of paramount importance - if they could read enigma traffic and direct convoys away from the u-boat wolf packs the cargo would arrive intact. Also, the British "huff duff" radio direction finding system helped to locate u-boats, as did sonar.
The gap was eventually closed by long range versions of the B24 Liberator, the u-boats had nowhere to hide, their captains were increasingly amazed that not only had they been found, they couldn't run. The so called "happy days" were over and life expectancy in the Kriegsmarine dropped significantly.
Some books you might find interesting:
Wartime Britain - Juliet Gardiner https://www.amazon.co.uk/Wartime-Britain-1939-1945-Juliet-Gardiner/dp/0755310284/ref=sr_1_1?ie=UTF8&qid=1476011630&sr=8-1 This is a general book of life in Britain at the time, it overs pretty much all aspects of life - being bombed, evacuation of children and of course rationing. It is a fantastic read if you want to get an idea of life at the time.
Battle Of The Atlantic - Marc Milner https://www.amazon.co.uk/Battle-Atlantic-Marc-Milner/dp/0752461877/ref=sr_1_9?ie=UTF8&qid=1476011593&sr=8-9 Covers the struggle of the battle and how the Allies eventually prevailed.
Enigma - The Battle For The Code - Hugh Sebag-Montefiore https://www.amazon.co.uk/Enigma-Battle-Cassell-Military-Paperbacks/dp/0304366625/ref=sr_1_1?ie=UTF8&qid=1476011644&sr=8-1 This covers the activities at Bletchley Park and the "back room" battle to gain access to the German military radio traffic. Whilst Naval Enigma is (of course) covered it does also cover the various other Enigma systems too.