The Bayesian Generalised Likelihood Uncertainty Estimation (GLUE) methodology, previously used in rainfall-runoff modelling, is applied to the distributed problem of predicting the space and time varying probabilities of inundation of all points on a flood plain. Probability estimates are based on conditioning predictions of Monte Carlo realizations of a distributed quasi-two-dimensional flood routing model using known levels at sites along the reach. The methodology can be applied in the flood forecasting context for which the N-step ahead inundation probability estimates can be updated in real time using telemetered information on water levels. It is also shown that it is possible to condition the Nstep ahead forecasts in real time using the (uncertain) on-line predictions of the downstream water levels at the end of the reach obtained from an adaptive transfer function model calibrated on reach scale inflow and outflow data.