Imported food results in a much larger carbon footprint, check where your food comes from and try and buy from as local as possible!
Eating a lot of meat, especially beef, results in a higher carbon footprint than eating non meat products. To reduce you carbon footprint, try to cut down on your meat consumption, or switch to a meat with a smaller footprint, like chicken
Chilled or frozen food require much more energy for storage (and hence a higher carbon footprint). Frozen foods also tend to be stored for longer and so will have accumulated a higher carbon footprint by the time they are consumed. If you are concerned about freshness, try buying local food from farmers markets!
Although not included in the food carbon footprint calculator, carbon may be emitted during transport to and from the supermarket. Try walking or cycling, home delivery has also been shown to result in lower emissions.
Organic food tends to have a lower carbon footprint, although this varies between individual foods, the biggest reductions are on milk, cheese and potatoes.