GROWING POTATOES IN BINS FOR THE FIRST TIME

Spuds like rich soil, but not to fertile or else the spuds can be damaged. Try earthing them up. Plant the spuds, when the shoots appear above soil by about 4-6 inch, carefully put more soil around the foliage untill its covered. Do this as much as the space allows.
Water wehn the flowers appear and dont let them dry out. When harvesting, there will be a lot more spuds because of this.

Carrots dont like fertile soil, but soil thats loose ish and have no stones ni. Fertiltiy will cause them to fork and become difficult to peel, ston and they wont grow striaght down and be short.

cabbages and things need a large area and probably wouldnt want to be in bins or boxes, could try sprouting brocolli if you can fing plug plants as you can keep harvesting the spears and it makes better use of space.
Tomatoes in hanging baskets, lettuce from seed around the base of the sprouts as it will be ready before the sprouts have got much bigger. Regular sowings will mean a continuos supply esp cut n come again.
Salad onions same, radish same, winter veg- mainly chinese veg mix, some winter lettuce you can over winter if kept frost free ish. You could grow sald veg in the used spud soil in the bins, just perhaps add some more compost and feed. Marshalls Seeds deal in veg and seeds, aslo find winter crops in there too.