The effect of an anomalous $\gamma W W$ coupling in the $e^{-} \gamma \rightarrow \nu_{e} W^{-}$ process through the angular and energy spectrum of the secondary leptons is investigated. Within the narrowwidth-approximation (NWA), a semianalytical study of the secondary lepton energy angle double distribution is considered. Different observables constructed using this distribution are expected to be very effective to probe the anomalous coupling at a typical International Linear Collider machine. Further, suitable combinations of these observables could be used to disentangle the effect of contributions from different terms in the effective Lagrangian.