Food production requires large amount of resources and is responsible for significant environmental impacts. One means to reduce these impacts is for consumers to change their diet, by selecting more sustainable food products. However, this is not a trivial task due to the variety of diets, food products and the need for behavioural change. This project considers how low-carbon diets could be achieved in an optimal way, requiring least departure from current diets and providing the required nutritional value. Multi-objective optimisation has been used for these purposes, considering global warming potential (GWP) and nutritional value of food and dietary changes that may be required. Focusing on the British case, three types of diet - one where all products including meat can be included, vegetarian and vegan - are considered and compared with the current diet. The results suggest significant reductions in GWP are possible if consumers are willing to change their diets, with reductions up to 50% being considered feasible. The results also suggest that changing the diet to meet government advice on nutrient intakes alone could lead to 5% reductions in the GWP of the diets for men, and 18% for women. Slightly greater changes to the diet, over and above those required to make the diet healthy, would result in much greater reductions in GWP (up to approximately 50%) whilst still being relatively easy to achieve. These changes include reducing or eliminating consumption of cheese, red meat and products high in sugar and fat. Changing to a vegetarian diet would reduce the GWP by 54% for men and 58% for women and changing to a vegan diet would reduce the GWP by 74% for both men and women on the current diet but would require drastic changes in consumer behaviour. Following government Eating-well Guide reduces the impact by 20% for men and 30% for women but it also requires significant behavioural changes. The findings of this project will be useful for those interested in promoting or following a healthy and low-carbon diets, including policy makers and consumers.