In this work, we present an approach to learn cost maps for driving in complex urban environments from a very large number of demonstrations of driving behaviour by human experts. The learned cost maps are constructed directly from raw sensor measurements, bypassing the effort of manually designing cost maps as well as features. When deploying the learned cost maps, the trajectories generated not only replicate human-like driving behaviour but are also demonstrably robust against systematic errors in putative robot configuration. To achieve this we deploy a Maximum Entropy based, non-linear IRL framework which uses Fully Convolutional Neural Networks (FCNs) to represent the cost model underlying expert driving behaviour. Using a deep, parametric approach enables us to scale efficiently to large datasets and complex behaviours by being run-time independent of dataset extent during deployment. We demonstrate the scalability and the performance of the proposed approach on an ambitious dataset collected over the course of one year including more than 25k demonstration trajectories extracted from over 120km of driving around pedestrianised areas in the city of Milton Keynes, UK. We evaluate the resulting cost representations by showing the advantages over a carefully manually designed cost map and, in addition, demonstrate its robustness to systematic errors by learning precise cost-maps even in the presence of system calibration perturbations.