Not really.

The Germans had a target of sinking ~300,000 tons of shipping each month in order to starve Britain, and overwhelm British/Allied ship production.

In the first 27 months of the war, Germany only hit that target 4 times. After that, when America joined the war and added their own production to the mix, they had to try and sink 700,000 tons, which they only did once for the rest of the war.

Only ~10% of convoys were ever attacked, so most got through without incident.

Rationing was definitely needed however, as whilst Britain could maintain enough food coming in to match rationing figures, it couldnt support the amount that had been coming in pre-war (especially given that trade from France and the European continent wasn't exactly booming). Pre-war was around 55 million tons of food, during the war was around 12 million. More focus was put on growing within the UK, so don't take those figures as the only food the UK had.

After 1943, the war started turning against the Germans, and with the breaking of Enigma, the Germans were often only able to sink a tenth of their shipping target. Despite this, the horifically poor state of the economy after the war as well as the costs of rebuiling, meant that rationing continued into the 1950's for some items. We didn't have much foreign currency left to but foreign food with, and years of shifting our economy to war production left a period of time when all that had to be shifted back to making things that the post-war era needed, before we could get the economy going properly again.

I can only be certain about the two first years of the war but no, Breat Britain was never critically close to a serious food shortage, even though they had begun rationing by 1940. This does not mean that there were no threat of food shortage. The problem for the government was that more than 70% of all food in Britain was important. This was no problem in peacetime, but Britain needed their ships for imports of steel, oil and other neccesary war materials. Therefor, it was of great importance that Great Britain improved their agriculture and food production. The problem was that Britain had chosen to focis on finished goods wich was valuable and they exported. This lead to a decline in agriculture, and this was not eaily reversed. Luckily for Britain a series of steps was taken to improve production in case of war. Among these were the reconstitution of the "Country Agriculture Commities", a new "Agriculture Act" was passed and the Minister of Agriculture began stockpiling of phosphates, oil seeds, cereal fields and even tractors. They were also investing in plowing more land and increasing mechanization of the farms, among other things. One advantage Britain had, was that the british prefferd mutton among meats. This was advantagous because sheep grazed on grass and they did not consume food that could be used feeding humans, in contrast to pigs who used the same foodstuffs as humans do. In addition the british produced alot of their meat themself, almost 50%. Admittably they still imported a lot of feedsuffs for ather animals. So in the end, Great Britain was very dependent on foreign imports and the biggest threat for the britsh was the german submarines. Admiral Dönitz was well aware of this and he reckoned that german submarines had to sink 500 000 tonnes of shipping each month within a year, and Great Britain would starve to death. In the beginning of the war the german submarines did sink over 350 000 tonnes a month, but this was not enough to see britain starve and britain had more than enough ships. There were multiple reasons why the U-boats never managed to sink enough merchant ships. The two most important was the lack of u-boats and the introduction of the convoy system. The first was a result of Hitler and the german navy high command, especially Admiral Raeder, Comander in chief of the Oberkommando der Marine, preffered the construction of a surface fleet, the Plan Z. In the eyes of Dönitz, who was the commanding germanys U-boats this was a complete waste of resources. in his eyes the Kriegsmarines goal should be to cut Britain from it's all important trade not winning a decisive victory. The Plan Z was scrapped when the war began, but by then it was all to late. By now the german had to few submarines to do the vital difference and they never managed to prodce enough U-boats to catch up. Although Germany tried to improve their U-boat production, this was hampered by Göring who was in charge of alocating resources. Göring was no fan of the fleet, and did not give enough resources to the construction of more U-boats. The introduction of the convoy system was also very important in diminishing the effectivness of the german U-boats. The convoys were a large number of ships sailing together. This alowed for better protection, safety in numbers. In addition they sailed with destroyer escorts and escorts of other vessels. This made it a lot harder for submarines to sink british shipping.

Also, there are more than one reason to begin rationing. In addition to begin rationing when you are low on food, it is also sensible to start when you expect to be low on food in the future or have a varying supply of food, such as imports.