We present a robust and real-time monocular six degree of freedom visual relocalization system. We use a Bayesian convolutional neural network to regress the 6-DOF camera pose from a single RGB image. It is trained in an end-to-end manner with no need of additional engineering or graph optimisation. The algorithm can operate indoors and outdoors in real time, taking under 6ms to compute. It obtains approximately 2m and 6 degrees accuracy for very large scale outdoor scenes and 0.5m and 10 degrees accuracy indoors. Using a Bayesian convolutional neural network implementation we obtain an estimate of the model's relocalization uncertainty and improve state of the art localization accuracy on a large scale outdoor dataset. We leverage the uncertainty measure to estimate metric relocalization error and to detect the presence or absence of the scene in the input image. We show that the model's uncertainty is caused by images being dissimilar to the training dataset in either pose or appearance.