There is increasing concern regarding the sustainability of global food production. It is unclear whether sustainable diets are healthy diets, and vice versa. The UK Government has declared its intention to achieve sustainable food procurement, but it is unclear whether this would lead to healthier foods provided in the public sector. In this thesis, I developed a method to quantify simultaneously the nutritional impact and carbon footprint of policies addressing sustainable and healthy diets using the primary school meals sector in England as an example. I systematically reviewed the literature to produce a list of the amounts of greenhouse gas emissions (GHGEs) in KgCO₂e associated with the production of a kilogram of different foods. These data were incorporated into a nutritional database (constructed from a dietary survey) - the Primary School Food Survey (PSFS) 2009 database. This dataset contains information on meals provided by schools and packed lunches from a representative sample of primary school children in England. GHGE values of individual food items from the systematic review were used to allocate a GHGE value for each food item included in the PSFS using a novel method. I analysed this dataset to present the current status of primary school meals with both nutritional and GHGE values. This analysis showed that a higher proportion of primary school lunches are healthier than packed lunches, when healthiness is defined as meeting nutrient-based standards for school foods - 64.5% of school lunches met at least 7 of the 14 standards compared to 43.2% of the packed lunches. But the mean GHGE value associated with a school lunch was slightly higher than packed lunches. Mena value (95% uncertainty interval) of a school lunch was 0.72 (0.71 - 0.74) compared to 0.70 (0.69 -0.71) KgCO2e. Incorporating uncertainty in GHGE parameters inflated the confidence intervals considerably. Scenario analyses showed that if primary school food sector in England achieves new food-based standards (published by the School Food Plan in July 2014) the proportion of meals achieving 7 or more nutrient-based standards would increase but the standards for saturated fat, salt and free sugars would be less likely to be achieved. The carbon foot print would also go up. If we adopt a 'Meat Free Mondays' policy, the proportion of meals achieving 7 or more nutrient-based standards will increase and the carbon foot print will be reduced. In both of those scenarios the nutrient-based standards for saturated fat, salt and non-milk extrinsic sugar are less likely to be achieved. Linear programming analyses showed that to construct a primary school meal which meets specific nutrient based standards with minimum GHGE values, it is possible to achieve a 40% reduction in GHGEs. The results of this thesis can be used to guide Government efforts to achieve healthy, sustainable food provision in primary schools and other sectors. The methods developed here can improve modelling studies that consider nutritional outcomes and sustainability outcomes simultaneously, particularly with regard to incorporating uncertainty into modelling results.