There's a rather good article on rationing here which addresses how it changed during the war. The system was planned from 1936, and had a surprising amount of flexibility in it. One of the main points was that it generally only covered foods for which a supply could be guaranteed, which meant that food rationing did not cover every food type. Also some foods were controlled by other means: bread, for instance, was not rationed until after the war, but the euphemistically named "wheatmeal" flour was introduced to reduce wastage by not removing all the bran.

Because not everything was rationed, there would be some legitimate local trade (more commonly through markets than directly with farmers) for items like vegetables. There was also what we might now call a grey market for things like rabbits. If you kept your own rabbits, you had to give up your meat ration - however these were not always registered, and hunted (or poached) rabbits would not fall under this rule anyway. Larger animals would be difficult to trade on the black market, since they had to be registered by the farmer.

There was also the parallel problem of cost. You might be able to acquire a rabbit legally, but you couldn't necessarily afford it. Most of the male work force were earning low wages in the armed forces, and home front wages were generally low. There was also an effective propaganda campaign to use food resources well, giving information on efficient means of cooking and eating - even down to the advice to eat your bread butter side down so that a smaller amount of butter would give the same taste.

Some of the habits from those days lasted a long time. When I grew up in the 60's and 70's, for instance, my mother would cook "Nothing Pie". It was a potato pie with a bit of onion in the mix, and a little cheese on the crust - a typical war time recipe, healthy and economical, but also designed to give as much taste and texture as possible from the limited resources. I still have the habit of eating "brown" (i.e. wheatmeal) bread rather than white, although this is getting a bit harder to find now as health-food types prefer wholemeal, and others go for the white bread which couldn't be bought during the War.

I'm interested in this also so I'll tack on my question. I remember reading in a mystery written around that time that a woman was selling veggies and eggs to make a little money or trade but that she didn't want a man from the rations to know about it. I think it was an Agatha Christie book, I'll look for it. It stuck with me because it seemed odd that they would get in trouble for trading with neighbors. So I would like to know too if they were forbidden to trade or buy from farmers, and if it was forbidden to buy or trade with them what was the penalty?