National infrastructure systems spanning energy, transport, digital, waste, and water are well recognised as complex and interdependent. While some policy makers have been keen to adopt the narrative of complexity, the application of complexity-based methods in public policy decision-making has been restricted by the lack of innovation in associated methodologies and tools. In this paper we firstly evaluate the application of complex adaptive systems theory to infrastructure systems, comparing and contrasting this approach with traditional systems theory. We secondly identify five key theoretical properties of complex adaptive systems including adaptive agents, diverse agents, dynamics, irreversibility, and emergence, which are exhibited across three hierarchical levels ranging from agents, to networks, to systems. With these properties in mind, we then present a case study on the development of a system-of-systems modelling approach based on complex adaptive systems theory capable of modelling an emergent national infrastructure system, driven by agent-level decisions with explicitly modelled interdependencies between energy, transport, digital, waste, and water. Indeed, the novel contribution of the paper is the articulation of the case study describing a decade of research which applies complex adaptive systems properties to the development of a national infrastructure system-of-systems model. This approach has been used by the UK National Infrastructure Commission to produce a National Infrastructure Assessment which is capable of coordinating infrastructure policy across a historically fragmented governance landscape spanning eight government departments. The application will continue to be pertinent moving forward due to the continuing complexity of interdependent infrastructure systems, particularly the challenges of increased electrification and the proliferation of the Internet of Things.