In 2015 the United Nations drafted the Paris Agreement and established the Sustainable Development Goals (SDGs) for all nations. A question of increasing relevance is the extent to which the pursuit of climate action (SDG 13) interacts both positively and negatively with other SDGs. We tackle this question through a two-pronged approach: a novel, automated keyword search to identify linkages between SDGs and UK climate-relevant policies; and a detailed expert survey to evaluate these linkages through specific examples. We consider a particular subset of SDGs relating to health, economic growth, affordable and clean energy and sustainable cities and communities. Overall, we find that of the 89 UK climate-relevant policies assessed, most are particularly interlinked with the delivery of SDG 7 (Affordable and Clean Energy) and SDG 11 (Sustainable Cities and Communities) and that certain UK policies, like the Industrial Strategy and 25-Year Environment Plan, interlink with a wide range of SDGs. Focusing on these climate-relevant policies is therefore likely to deliver a wide range of synergies across SDGs 3 (Good Health and Well-being), 7, 8 (Decent Work and Economic Growth), 9 (Industry, Innovation and Infrastructure), 11, 14 (Life Below Water) and 15 (Life on Land). The expert survey demonstrates that in addition to the range of mostly synergistic interlinkages identified in the keyword search, there are also important potential trade-offs to consider. Our analysis provides an important new toolkit for the research and policy communities to consider interactions between SDGs, which can be employed across a range of national and international contexts.