Food systems contribute 23–42% of global greenhouse gas emissions. Reducing food system emissions is an essential component of climate change mitigation, and a system-wide approach, including production, processing, trade and demand-side transformations, will be needed. Long-term analysis of greenhouse gas (GHG) emissions of food supply is crucial for informing this transformation, and understanding the processes contributing to existing trends can reveal opportunities for future mitigation strategies. To address these needs we used data on food supply, trade and emission intensity to quantify changes in GHG emissions between 1986 and 2017 resulting from food supply in the United Kingdom (UK). Uniquely, the relative contributions of supply-side and demand-side changes to historical trends in food emissions were assessed, and the gap between current UK food consumption and EAT-Lancet recommended diets was used to estimate the additional GHG emission reductions that could be achieved by shifting to the Planetary Health Diet (PHD). It was estimated that in the UK, per-capita GHG emissions from food fell by 32% (from 4.6 tCO2eq/capita to 3.1 tCO2eq/capita) between 1986 and 2017. Of this 32% reduction, 21% was due to supply-side changes (a fall in emission intensity per unit of production due to increased efficiency of farming practices), 10% was due to demand-side changes (including dietary change and waste reduction), and 2% was due to changing trade patterns. Relative to the PHD, however, the average UK citizen still greatly over-consumes beef, lamb and pork, tubers and starchy vegetables and dairy products, and under-consumes vegetables, nuts, and legumes. It was estimated that by adopting the PHD, UK per capita food emissions could be reduced by a further 42% to 1.8 tCO2eq/capita. These results expose the historic contributions of both supply- and demand-side changes to reductions in GHG emissions from food, and highlight the underutilised potential of dietary change in contributing to mitigation of GHG emissions from food.