Estimates of various characteristics of extreme sea currents, such as speeds and their directions, are required when designing offshore structures. This paper extends standard statistical methods for extreme values to handle the directionality, temporal dependence and tidal non-stationarity that are present in sea current extremes. The methods are applied to a short period of data from the Inner Dowsing Light Tower in the North Sea. Substantial benefits, over existing methods, are obtained from our analysis of the sea current by decomposing it into tide and surge currents. In particular, we find that at the Inner Dowsing the strong directionality in extreme sea current speeds is completely explained by the tidal current and directionality in the non-extreme surge currents. This finding aids model fitting and extrapolation.