It depends upon the definition of contribution and necessary. There were about 1.5 million garden allotments and over half of the UK's manual laborers kept a private garden. The Ministry of Food actively encouraged the cultivation and consumption of privately-grown vegetables. Part of this push by the government was due to the fears of nutritionists that wartime rationing would have a negative impact on the UK's population. The Ministry of Food's campaigns to educate the public on the importance of vegetables and vitamins, leading to a popularization of myths like carrots promote good eyesight. Yet, if one could ignore the pun, these efforts of the government bore fruit. The UK citizens ate an unprecedented amount of vegetables during the war and public awareness of nutrition increased.

The wider impact of Dig for Victory on the war effort was two-fold. The increase in nutrition provided by vegetable supplements helped make the UK's rationing effort more efficient. The increased caloric and nutritional benefit created by private gardens helped make the UK's working population more able to work longer hours without detrimental effects upon total health. Secondly, vegetable gardens helped morale. The rationing of the Ministry of Food was acceptable, but made for a very plain and tedious meals. The fresh produce alleviated some of the monotony of bread and potatoes with very little meat or meager amounts of dairy. UK homemakers became slightly adept during the war at using this fresh produce to create new dishes or ersatz replacements for scarce food luxuries. One of the most prized and difficult crops for UK gardeners to grow were onions. The U-boat blockade and German occupation of Western Europe had severely cut imports of onions to the UK and the Ministry of Food's attempt to cultivate commercial production of onions through the Vegetable Marketing Company was a failure. Although UK gardeners found it difficult to grow onions, a successful home crop greatly flavored the rationing staples of bread and potatoes.

While the Dig for Victory campaign was not essential for victory, it made the British home front much easier to bear. This was in stark contrast to the Axis powers late in the war, occupied areas, and the USSR, where the private cultivation of food was sometimes a matter of life or death for the civilian population. Wartime pressures in these countries meant that garden plots were essential to prevent starvation or chronic malnutrition. In this sense, the UK gardeners had the relative luxury of gardening which made the pressures of war slightly more bearable.

Source

Collingham, E. M. The Taste of War: World War II and the Battle for Food. New York: Penguin Press, 2012.

Oddly, I was just watching "The World At War" earlier and it mentioned the "saucepans into Spitfires" campaign as having been more of a morale-booster than any practical help. I had been going to ask here what became of all those pots, pans, bathtubs etc - did they get used for something (albeit less glamorous than Spitfires), or was it a total waste from a material point of view?

Survived, yes I presume so.

First, vegetables and fruit were never rationed. However, they could be scarce and a black market sprung up and they could be sold "above the [government] fixed price or in greater quantity than was allowed to favoured customers".

But did the extra produce produced (and in very small part meat also - rabbits and chickens mostly) help? I can't see how not. The nutrients from the fresh fruit and veg produced by allotmenteers as well as from the pleasure gardens that were dug up for veg gardens I'm sure helped take the edge off some peoples' hunger.

Officially, the programs were declared a success, over and over. But a lot of the figures that were reported at the time to back this up seem a bit suspect. "After the 1942-3 season, a gardening paper calculated that almost 1,000,000 tons of vegetables had been produced on allotments, which is rather more than half a ton per allotment. In the light of the Ministry's findings, this seems unlikely". The Dig for Victory campaign itself had only a small effect. Of the 55.2% of households that grew veg during a 1942 survey, only 16% of those with a allotment attributed their lease to the publicity campaign. "According to The Gardener's Chronicle, in December 1944 the annual value of produce [on allotments] was, apparently, £17,250,000. This cannot possibly have been accurately calculated".

For all the great anecdotal stories told in the papers of the time and the staying power the phrase has, gardening did not much reduce the purchase of commercial fruit and veg. "The surveyors measured the number of ounces of various vegetables eaten by each person in a week. With the exception of potatoes, cabbages and rhubarb, there was no very great difference in the amount that gardeners and non-gardeners bought in the shops".

It seems the British were using these programs and their "results" in part, as propaganda. There may not have been deliberate misleading of the public, but less-than-impressive survey results were not made public, and media of the time did all it could to present itself as patriotic, so the "records" are definitely biased.

That is not to say that some individuals didn't believe that they were contributing to the war effort. The idea was that the more that could be produced and consumed in the country, the more that would be able to be sent to the boys on the war front. As buying habits showed, this was mostly not true.

In addition, since the government did not seem to think beyond encouraging people to grow food, there was some wastage. Especially when people planted what they liked instead of following the recommended crops and cropping timetables. Imagine the inevitable pile of courgettes (zuccini) that cannot all be eaten nor given away. This was especially so because inexperienced gardeners were being encouraged to take up he spade. And the allure of growing cabbage for the wintertime is not the same as growing some nice lettuce for right now. Even though the government released informational brochures to try to address this issue, the impact was minor.

There are some reliable figures for a related government encouraged activity: jam making. The Ministry of Agriculture organized the WI to process a glut of plums in 1940 into jam for the British sweet tooth. They did so with 1,631 tons of the fruit. This in times when sugar was heavily rationed. The impressive numbers continued throughout the war. In 1941 they made 1,630 tons of preserve. Only in 1945 with a late spring frost did the number of canning locations finally begin to drop. From 1940-1945 more than 5,300 tons of fruit (~12 million lbs) of fruit was preserved. However, all this work accounted for "less than 0.5% of the national requirement for (rationed) jam in the wartime, so the effort was largely symbolic".

The numbers in the long run are especially telling. The roughly 1.75 million wartime allotments dropped by a half million by 1947 even though rationing was still pretty intense (the potato wasn't even rationed until 1947 and bread was rationed until 1948). The advantage of growing your own could not have been that strong to see such a drop off.

One of the long term effects of the government programs to consider is that Ribena was issued to children to make up for vitamin C lost because citrus fruits were no longer readily available. That certainly helped cement its place in the culture for years, at least until the GSK scandal of 2004-2007. But Ribena probably did not help win the war.

General impressions and all quotes are from "A Green and Pleasant Land: How England's Gardeners Fought the Second World War" by Ursula Buchan.

I'd like to know whether Victory Gardens did anything in the USA, maybe a comparison too?