Background: Average population dietary intakes do not reflect the wide diversity of dietary patterns across the population. It is recognised that most people in the UK do not meet dietary recommendations and have diets with a high environmental impact, but changing dietary habits has proved very difficult. The purpose of this study was to investigate the diversity in dietary changes needed to achieve a healthy diet and a healthy diet with lower greenhouse gas emissions (GHGE) (referred to as a sustainable diet) by taking into account each individual’s current diet and then minimising the changes they need to make. Methods: Linear programming was used to construct two new diets for each adult in the UK National Diet and Nutrition Survey (n = 1491) by minimising the changes to their current intake. Stepwise changes were applied until (i) dietary recommendations were achieved and (ii) dietary recommendations and a GHGE target were met. First, gradual changes (≤50 %) were made to the amount of any foods currently eaten. Second, new foods were added to the diet. Third, greater reductions (≤75 %) were made to the amount of any food currently eaten and finally, foods were removed from the diet. Results: One person out of 1491 in the sample met all the dietary requirements based on their reported dietary intake. Only 7.5 and 4.6 % of people achieved a healthy diet and a sustainable diet, respectively, by changing the amount of any food they currently ate by up to 50 %. The majority required changes to the amount of each food eaten plus the addition of new foods. Fewer than 5 % had to remove foods they ate to meet recommendations. Sodium proved the most difficult nutrient recommendation to meet. The healthy diets and sustainable diets produced a 15 and 27 % reduction in greenhouse gas emissions respectively. Conclusions: Since healthy diets alone do not produce substantial reductions in greenhouse gas emissions, dietary guidelines need to include recommendations for environmental sustainability. Minimising the shift from current dietary intakes is likely to make dietary change more realistic and achievable