Here is a list of which vegetables, according to the food website Eat the Seasons, are in season and when:
January – beetroot, brussels sprouts, parsnip, apples
February – cauliflower, chicory, leeks, pears
March – purple sprouting broccoli, rhubarb, spring onions
April – jersey royal new potatoes, radishes, watercress
May – asparagus, spinach, spring onions
June – artichoke, carrots, courgettes, runner beans
July – broad beans, cucumber, onions
August – peas, potatoes, raspberries, plums
September – butternut squash, marrow, blackberries
October – celery, kale, chestnuts, elderberries
November – pumpkin, swede, quince, walnuts
December – turnips, leeks, apples