My previous house came with a backyard so small you could barely swing a medium-sized rodent, let alone a cat. At first I didn't think I could successfully grow stuff. Twelve months later my backyard contained a wide variety of pots acquired from car-booting, skips and recycling/salvage yards plus a mini-growhouse. The growhouse held a growbag just large enough for 1 x tomato plant, 1 x cucumber plant & 1 x capsicum plant.
In the pots I successfully grew dwarf french beans, runner beans (a great example of vertical gardening), carrots, leeks, spring onions, mini beetroot, lettuce, strawberries and peas. Several pots held two crops whilst others held a crop plus a flower.
In a four foot square space I fitted twenty potato growbags, each holding one tuber. Although the potatoes didn't grow very big, they were well tasty.
I found a very useful book on cottage gardening and seeing what the gardeners of a 100+ years ago fitted into a small space is amazing.
CC