The increasing interest in autonomous marine systems and related applications has motivated, among others, the development of systems and algorithms for the dynamic positioning of underactuated marine vehicles (ships, surface vessels and underwater vehicles) under the influence of unknown environmental disturbances. In this paper, we present a state feedback control solution for the navigation and practical stabilisation of an underactuated marine vehicle under non-vanishing current disturbances, by means of hybrid control. The proposed solution involves a logic-based switching control strategy among simple state feedback controllers, which renders the position trajectories of the vehicle practically stable to a goal set around a desired position. The control scheme consists of three control laws; the first one is active out of the goal set and drives the system trajectories into this set, based on a novel dipolar vector field. The other two control laws are active in the goal set and alternately regulate the position and the orientation of the vehicle, so that the switched system is practically stable around the desired position. The overall system is shown to be robust, in the sense that the vehicle enters and remains into the goal set even if the external current disturbance is unknown, varying and only its maximum bound (magnitude) is given. The efficacy of the proposed solution is demonstrated through simulation results.