Suboptimal diet is a leading risk factor for early death and disability globally. Changing food prices via tax or subsidy policies is often recommended to improve diets, particularly increasing the relative price of sugar-sweetened beverages to reduce sugar consumption. Less evidence exists on how such policies, if applied across a wide range of foods and beverages, could affect purchases and diet quality. Using home-scan data from a sample of 26,799 households in Great Britain (2012-2013) we estimate separate demand elasticities for price increases and decreases using a reference-price dependent demand model, to simulate the impact of a 20% price change on purchases of energy and nutrients from 26 healthier and less healthy food groups that make up the full basket of purchases. Where asymmetry exists between elasticity of price increase and decrease, household response to price increases is stronger. Households with low socio-economic status (SES) respond to price changes in either direction more strongly than high-SES, especially for less healthy foods. On average, energy and nutrient content of take-home purchases were near or above reference daily intake levels. The combined effect of increasing the price of all less healthy foods, and decreasing the price of all healthier foods, led to an overall improvement with a net reduction in energy (by 67.6kcal per capita/day), sugar (6.3g), salt (0.21g) and saturated fat (2.3g) content, and a net increase in protein (3.4g) and fibre (0.9g) content of purchases. From individual food groups, the greatest reduction in energy, sugar and saturated fat content was observed for price increases in sweet snacks, desserts and puddings, and fats and oils. Dietary quality of the purchases of low-SES households generally improved most. Our findings support the view that price change policies can lead to dietary improvements, if they are based on the healthiness of food and beverages.