I want a small veggie garden but can't physically make a garden as land lord won't allow it?

With the souring costs of fruit and veg due to the drought I was thinking of making a veggie garden, however I live in a block of flats with a shared backyard so for that reason can't make a veggie garden in the ground, I'm looking to grow potatoes, tomatoes and carrots is it possible to grow vegetables in a cardboard box?