Extreme weather causes substantial adverse socio-economic impacts by damaging and disrupting the infrastructure services that underpin modern society. Globally, $2.5tn a year is spent on infrastructure which is typically designed to last decades, over which period projected changes in the climate will modify infrastructure performance. A systems approach has been developed to assess risks across all infrastructure sectors to guide national policy making and adaptation investment. The method analyses diverse evidence of climate risks and adaptation actions, to assess the urgency and extent of adaptation required. Application to the UK shows that despite recent adaptation efforts, risks to infrastructure outweigh opportunities. Flooding is the greatest risk to all infrastructure sectors: even if the Paris Agreement to limit global warming to 2°C is achieved, the number of users reliant on electricity infrastructure at risk of flooding would double, while a 4°C rise could triple UK flood damage. Other risks are significant, for example 5% and 20% of river catchments would be unable to meet water demand with 2°C and 4°C global warming respectively. Increased interdependence between infrastructure systems, especially from energy and information and communication technology (ICT), are amplifying risks, but adaptation action is limited by lack of clear responsibilities. A programme to build national capability is urgently required to improve infrastructure risk assessment.