Localised erosion (scour) during flood flow conditions can lead to costly damage or catastrophic failure of bridges, and in some cases loss of life or significant disruption to transport networks. Here, we take a broad scale view to assess risk associated with bridge scour during flood events over an entire infrastructure network, illustrating the analysis with data from the British railways. There have been 54 recorded events since 1846 in which scour led to the failure of railway bridges in Britain. These events tended to occur during periods of extremely high river flow, although there is uncertainty about the precise conditions under which failures occur, which motivates a probabilistic analysis of the failure events. We show how data from the historical bridge failures, combined with hydrological analysis, have been used to construct fragility curves that quantify the conditional probability of bridge failure as a function of river flow, accompanied by estimates of the associated uncertainty. The new fragility analysis is tested using flood events simulated from a national, spatial joint probability model for extremes in river flows. The combined models appear robust in comparison with historical observations of the expected number of bridge failures in a flood event, and provide an empirical basis for further broad-scale network risk analysis.