This work studies the development of a sustainable hydrogen infrastructure that supports the transition towards a low-carbon transport system in the United Kingdom (UK). The future hydrogen demand is forecasted over time using a logistic diffusion model, which reaches 50% of the market share by 2070. The problem is solved using an extension of SHIPMod, an optimisation-based framework that consists of a multi-period spatially-explicit mixed-integer linear programming (MILP) formulation. The optimisation model combines the infrastructure elements required throughout the different phases of the transition, namely economies of scale, road and pipeline transportation modes and carbon capture and storage (CCS) technologies, in order to minimise the present value of the total infrastructure cost using a discounted cash-flow analysis. The results show that the combination of all these elements in the mathematical formulation renders optimal solutions with the gradual infrastructure investments over time required for the transition towards a sustainable hydrogen economy. (C) 2016 The Authors. Published by Elsevier Ltd.