Natural hazards have the potential to trigger complex chains of events in technological installations leading to disastrous effects for the surrounding population and environment. The threat of climate change of worsening extreme weather events exacerbates the need for new models and novel methodologies able to capture the complexity of the natural-technological interaction in intuitive frameworks suitable for an interdisciplinary field such as that of risk analysis. This study proposes a novel approach for the quantification of risk exposure of nuclear facilities subject to extreme natural events. A Bayesian Network model, initially developed for the quantification of the risk of exposure from spent nuclear material stored in facilities subject to flooding hazards, is adapted and enhanced to include in the analysis the quantification of the uncertainty affecting the output due to the imprecision of data available and the aleatory nature of the variables involved. The model is applied to the analysis of the nuclear power station of Sizewell B in East Anglia (UK), through the use of a novel computational tool. The network proposed models the direct effect of extreme weather conditions on the facility along several time scenarios considering climate change predictions as well as the indirect effects of external hazards on the internal subsystems and the occurrence of human error. The main novelty of the study consists of the fully computational integration of Bayesian Networks with advanced Structural Reliability Methods, which allows to adequately represent both aleatory and epistemic aspects of the uncertainty affecting the input through the use of probabilistic models, intervals, imprecise random variables as well as probability bounds. The uncertainty affecting the output is quantified in order to attest the significance of the results and provide a complete and effective tool for riskinformed decision making.