Rapid deterministic modelling of shoreline evolution at regional and coastal-scheme scale enables Monte-Carlo simulations by which long-term shoreline statistics can be estimated. This paper describes UnaLinea, a fast, accurate finite difference solver of the one-line sediment continuity equation. The model is verified for the evolution of an initially straight shoreline of a plane beach subject to regular breaking waves at constant angle of incidence in the presence of either a groyne or a continuous single-point feed of sediment. Grid convergence and stability tests are used to obtain accurate, stable results, with satisfactory computational efficiency. Influences of wave input filtering and event-based sediment loading are considered. The rapid deterministic model is applied to Monte-Carlo simulations of the evolution of the west coast of Calabria, Italy for different scenarios including increased sediment load from a river and selected beach nourishment. The potential role of probabilistic shoreline evolution in regional coastal flood-risk assessment is explored through application to an idealised stretch of the Holderness coastline, U.K., where flood depths and expected damage are estimated for a 1000 year return period event.