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Recent extreme weather events have had severe impacts on UK crop yields, and so there is concern that a greater frequency of extremes could affect crop production in a changing climate. Here we investigate the impacts of future climate change on wheat, the most widely grown cereal crop globally, in a temperate country with currently favourable wheat-growing conditions. Historically, following the plateau of UK wheat yields since the 1990s, we find there has been a recent significant increase in wheat yield volatility, which is only partially explained by seasonal metrics of temperature and precipitation across key wheat growth stages (foundation, construction and production). We find climate impacts on wheat yields are strongest in years with compound weather extremes across multiple growth stages (e.g. frost and heavy rainfall). To assess how these conditions might evolve in the future, we analyse the latest 2.2 km UK Climate Projections (UKCP Local): on average, the foundation growth stage (broadly 1 October to 9 April) is likely to become warmer and wetter, while the construction (10 April to 10 June) and production (11 June to 26 July) stages are likely to become warmer and slightly drier. Statistical wheat yield projections, obtained by driving the regression model with UKCP Local simulations of precipitation and temperature for the UK's three main wheat-growing regions, indicate continued growth of crop yields in the coming decades. Significantly warmer projected winter night temperatures offset the negative impacts of increasing rainfall during the foundation stage, while warmer day temperatures and drier conditions are generally beneficial to yields in the production stage. This work suggests that on average, at the regional scale, climate change is likely to have more positive impacts on UK wheat yields than previously considered. Against this background of positive change, however, our work illustrates that wheat farming in the UK is likely to move outside of the climatic envelope that it has previously experienced, increasing the risk of unseen weather conditions such as intense local thunderstorms or prolonged droughts, which are beyond the scope of this paper. [ABSTRACT FROM AUTHOR]