A requirement for new sources of flexibility in meeting energy demand and the growing interest in the interaction between energy sectors have drawn attention to multi-energy systems, which can offer numerous benefits, e.g. providing flexibility to counteract the intermittency of renewable generation and increase energy efficiency. In order to maximise these benefits, advanced control methods are required. The model predictive control methodology is a promising candidate for such applications as it is capable of incorporating economic and operational objectives whilst respecting various technical, regulatory and environmental constraints. In order to implement such a control strategy effectively, it is necessary to develop appropriate system models. This paper presents a novel generalised modelling framework for multi-energy systems that is particularly well suited, though not limited to, predictive control applications. The proposed approach is capable of representing energy converter arrangements of arbitrary complexity containing multiple energy vectors, as well as multi-directional energy flow, multi-generation and multi-mode devices, a wide range of controllable producers/consumers, energy storage and flexible loads. The effectiveness of the approach is demonstrated using a representative case study based on three buildings at the University of Manchester where the developed model is incorporated into a model predictive control scheme. The simulation results show how the controller minimises the cost of purchasing energy whilst satisfying operational constraints, and managing various types of flexible demand.