Providing you grow 'intensive' a relatively small vegetable plot will provide many of the vegetables required for the year.
Much depends upon the crops that you grow. Potatoes for instance, will take up a lot of space. Other than the first earlies, they are relatively cheap at the supermarket - even the organic ones.
The crops that really can keep you supplied for the year without taking too much space, include Carrots, all salad crops including tomatoes, runner beans up a cane tent - wigwam - or along a fence, onions, leaf beet spinach, perpetual spinach, to name just a few.
The secret, is not to grow vegetables in the traditional rows, go for batch planting with a few stepping stones, make sure that you have a succession programme, and intercropping!
Vegetables can mostly be grown quite close together, so make as much use of available space. No bare earth showing anywhere - even in the winter months!