The Met Office is tasked with developing a detailed uncertainty analysis for future climate, as part of a UK-wide climate change risk assessment, in order to meet the requirements of the Climate Change Act, 2008, which constructed a legally-binding long-term framework for building the UK’s ability to adapt to a changing climate. This analysis exploited a general methodology for the Bayesian analysis of uncertainty for complex physical systems modelled by computer simulators. This report describes the general mathematical structure, its role in climate uncertainty assessment and the impacts, both statutory and in applications, arising from such climate projections.