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Understanding how renewable energy generation affects electricity prices is essential for designing efficient and sustainable electricity markets. However, most existing studies rely on regression-based approaches that capture correlations but fail to identify causal relationships, particularly in the presence of non-linearities and confounding factors. This limits their value for informing policy and market design in the context of the energy transition. To address this gap, we propose a novel causal inference framework based on local partially linear double machine learning (DML). Our method isolates the true impact of predicted wind and solar power generation on electricity prices by controlling for high-dimensional confounders and allowing for non-linear, context-dependent effects. This represents a substantial methodological advancement over standard econometric techniques. Applying this framework to the UK electricity market over the period 2018-2024, we produce the first robust causal estimates of how renewables affect day-ahead wholesale electricity prices. We find that wind power exerts a U-shaped causal effect: at low penetration levels, a 1 GWh increase reduces prices by up to £7/MWh, the effect weakens at mid-levels, and intensifies again at higher penetration. Solar power consistently reduces prices at low penetration levels, up to £9/MWh per additional GWh, but its marginal effect diminishes quickly. Importantly, the magnitude of these effects has increased over time, reflecting the growing influence of renewables on price formation as their share in the energy mix rises. These findings offer a sound empirical basis for improving the design of support schemes, refining capacity planning, and enhancing electricity market efficiency. By providing a robust causal understanding of renewable impacts, our study contributes both methodological innovation and actionable insights to guide future energy policy.