In this paper we consider the problem of cooperative vehicle localisation, in which a group of vehicles are driving in an outdoor environment, each estimating their position using a global positioning system (GPS) and odometry. Additionally, the vehicles can improve their estimates by observing positions of other vehicles using a proximity sensor, such as a radar, and a mutual communication, which is especially helpful to those vehicles operating in areas with no GPS coverage. In a distributed fusion system, each vehicle needs to account for the fact that information received from other vehicles might originate in part from the vehicle itself, resulting in a correlation between the state estimate and observation errors. This problem, also known as data incest, is amplified by the dynamic and unstructured nature of the communication topology, inherent to a cooperative localisation scenario. We provide a novel solution to the problem based on the Common Past-Invariant Ensemble Kalman filter (CPI-EnKF) - a generalisation of the Ensemble Kalman filter that can be applied in the presence of common past information shared between the state estimate and the observation, which has been recently proposed by this paper's authors. As we will demonstrate, the CPI-EnKF is simpler to apply, provides better estimates, can be scaled to an arbitrary number of vehicles and is computationally more efficient than other similar methods.