Navigation in pedestrian populated environments is a highly challenging task, and a milestone on the way to fully autonomous urban driving systems. Pedestrian populated environments are highly dynamic, uncertain and difficult to predict. The strict safety measures in such environments result in overly reactive navigation systems, which do not match the conduct of experienced drivers. An autonomous vehicle driving alongside pedestrians should convey a natural and a socially-aware behaviour. Therefore, the vehicle should not merely react to the behaviour of the surrounding agents, but should rather cooperate and proactively interact with its surrounding. Excluding this aspect from the navigation scheme results in over-reactive behaviours, an unnatural driving pattern and a suboptimal navigation solution. This paper presents a proactive longitudinal velocity control method, appropriate for navigation in close interaction with pedestrians. The work uses a cooperation-based pedestrians-vehicle behavioural model to find the optimal longitudinal velocity control. The method is implemented in lateral crossing scenarios with a dense crowd of pedestrians. The results are then compared with a reactive navigation system. The method is evaluated in terms of the vehicle's travel time and the safety of the pedestrians in the scene.