The Harmonised Monitoring Scheme (HMS) records are the best long-term data sets for river water quality in Britain. A simple framework for statistical analysis of these data is developed which copes with the many observations below the limits of detection of the laboratory analytical methods used to measure concentrations of chemical determinands. Besides the estimates of annual mean concentrations, two products of the framework are estimates of precision of these means and a test of long-term change in annual mean concentration. The methodology is applied to concentrations of ammoniacal nitrogen, chloride, nitrite, nitrate, orthophosphate, copper and zinc at HMS river sites in England and Wales. These sites show a clear net improvement in ammoniacal nitrogen, nitrite, copper and zinc concentrations when comparing the late-1970s with the early-1990s. Conversely, between the same two periods, these sites show a clear net deterioration in chloride and orthophosphate concentrations and a small net deterioration in nitrate concentration at the HMS river sites. The simple framework is extended to include a seasonal component and a full likelihood test of long-term change. This is applied to ammoniacal nitrogen concentration at 30 HMS sites. The proportion of sites showing long-term improvement in ammoniacal nitrogen is a little higher than that obtained in the simple framework, suggesting that the simple approach is conservative in detecting change.