Laboratory experiments were performed to study the dynamics of three-dimensional mechanically generated waves propagating over an oblique current in partial opposition. The flow velocity varied along the mean wave direction of propagation with an increasing trend between the wave-maker and the centre of the tank. Tests with regular wave packets traversing the area of positive current gradient showed that the concurrent increase of wave steepness triggered modulational instability on otherwise stable wave trains and hence induced the development of very large amplitude waves. In random directional wave fields, the presence of the oblique current resulted in a weak reinforcement of wave instability with a subsequent increase of the probability of occurrence of extreme events. This seems to partially compensate the suppression of strongly non-Gaussian properties due to directional energy distribution.