The UK government launched a two-component sugar-reduction programme in 2016, one component is the taxation of sugar-sweetened beverages, the Soft Drinks Industry Levy (SDIL), and the second is a voluntary sugar reduction programme for products contributing most to children’s sugar intakes. These policies provided incentives both for industry to change the products they sell, and for people to change their food and beverage choices through a “signalling” effect that has raised awareness of excess sugar intakes in the population. In this study, we aimed to identify the relative contributions of the supply- and demand-side drivers of changes in the sugar density of food and beverages purchased in Great Britain. While we found that both supply- and demand-side drivers contributed to decreasing the sugar density of beverage purchases (reformulation led to a 19% reduction, product renewal 14%, and consumer switching between products 8%), for food products it was mostly supply-side drivers (reformulation and product renewal). Reformulation contributed consistently to a decrease in the sugar density of purchases across households, whereas changes in consumer choices were generally in the opposite direction, offsetting benefits of reformulation. We also studied the social gradient of sugar density reduction for breakfast cereals, achieved mostly by reformulation, and found increased reductions in sugar purchased by households of lower socioeconomic status. Conversely, there was no social gradient for soft drinks. We conclude that taxes and reformulation incentives are complementary and combining them in a programme to improve the nutritional quality of foods increases the probability of improvements in diet quality.