Sustainable diets are defined as “nutrient-dense, affordable, culturally acceptable, and sparing of the environment” (Drewnowski, 2017). Whilst diets which cover the nutrient and environmental aspects have been studied in detail, there has been little work on also incorporating acceptability (i.e. consumer preferences). This study estimates sustainable diets using the Green et al (2015) dietary models (quadratic programming based) with the following data: national diet and nutrition survey, dietary reference values, Kantar Worldpanel prices and carbon footprints. The diet models were estimated for eight UK demographic groups alongside estimation of the respective demand systems in order to incorporate own price elasticities. The results suggest that sustainable diets for all the demographic groups are to an extent possible based on the nutrient constraints used, with the largest emission reductions (relative to the baseline diet emissions) of 45 per cent for males aged 19 to 50 and aged 50 plus.