The European Union’s Green Deal proposal and Farm to Fork strategy call for both demand and supply measures to reduce emissions from the food system. While research clearly illustrates the importance of dietary transitions, impacts of potential supply-side measures are not well understood in relation to competitiveness concerns and leakage effects. This study assesses trade and GHG emission impacts of two supply-side mitigation strategies (intensification vs. extensification) in the EU, UK and Switzerland (EU + 2), against a 2050 baseline featuring healthy/sustainable diets adopted by European consumers. To capture potential leakage effects arising from changing external trade flows, the two supply-side strategies are assessed against three trade policy regimes (i.e. status quo, regional trade liberalization with and without border carbon adjustment), resulting in six scenarios formulated with detailed inputs from the EUCalc model and other literature and simulated with a purported-designed CGE model. Results show that intensification, while improving the EU + 2’s external trade balance, does not reduce emissions in the EU + 2, compared to the baseline. In contrast, extensification leads to a substantial emission abatement that augments reductions from the assumed dietary transition in the baseline, resulting in a combined 31% agricultural emission reduction in EU + 2 during 2014–2050. However, this is at the expense of reduced net agrifood exports by US$25 billion compared to the baseline and significant carbon leakage at a rate of 48% (i.e. nearly half of agricultural emission reduction in the EU + 2 ‘leaked’ to elsewhere). Furthermore, implementing the EU + 2’s prospective regional trade agreements results in increased territorial emissions. Although a border carbon adjustment by the EU + 2 can improve its trade balance and partially shift mitigation burdens to other countries, the associated reductions in global emissions (and carbon leakage) would be marginal. Finally, different trade and emission effects are identified between the crop and livestock sectors, pointing to the desirability of a mixed agriculture system with intensified livestock sector and extensified crop agriculture in the EU + 2 that balances emission reduction goals and competitiveness concerns.