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Domain generalisation aims to promote the learning of domain-invariant features while suppressing domain-specific features, so that a model can generalise better to previously unseen target domains. An approach to domain generalisation for object detection is proposed, the first such approach applicable to any object detection architecture. Based on a rigorous mathematical analysis, we extend approaches based on feature alignment with a novel component for performing class conditional alignment at the instance level, in addition to aligning the marginal feature distributions across domains at the image level. This allows us to fully address both components of domain shift, i.e. covariate and concept shift, and learn a domain agnostic feature representation. We perform extensive evaluation with both one-stage (FCOS, YOLO) and two-stage (FRCNN) detectors, on a newly proposed benchmark comprising several different datasets for autonomous driving applications (Cityscapes, BDD10K, ACDC, IDD) as well as the GWHD dataset for precision agriculture, and show consistent improvements to the generalisation and localisation performance over baselines and state-of-the-art.