In a resource-constrained world with growing population and demand for energy, goods, and services with commensurate environmental impacts, we need to understand how these trends relate to aspects of economic activity. We present a computational model that links energy demand through to final economic consumption, illustrated by application to UK data. Our model fits within a whole-economy framework which harmonises multiple national accounting procedures. Our model minimises both the number of exogenous aspects and tuning factors by using historical data to calibrate relationships. We divide economic activity into a number of distinct but interdependent outputs that are non-substitutable in the short-term. The dynamic aspects assume that supply follows demand, but are constrained in the short-term by physical infrastructure. At the same time, capital formation grows the physical infrastructure. Our model regenerates historical data dynamically as a basis for projecting forward scenarios to discuss pathways to a lower carbon future.