For the co-ordination of flood mitigation activities and for the insurance and re-insurance industries, knowledge of the spatial characteristics of fluvial flooding is important. Past research into the spatio-temporal risk of fluvial flooding is restricted to empirical estimates of risk measures and hence estimates cannot be obtained for return periods longer than the length of the concurrent data at the sites of interest in the sample. We adopt a model-based approach which describes the multisite joint distribution of daily mean river flows and daily precipitation totals. A measure of spatial dependence is mapped across Great Britain for each variable separately. Given that an extreme event has occurred at one site, the measure characterises the extent to which neighbouring locations are affected. For both river flow and precipitation we are able to quantify how events become more localised in space as the return periods of these events get longer at a site of interest. For precipitation, spatial dependence is weaker in the upland areas of Great Britain. For river flows the major factor affecting spatial dependence appears to be differences in catchment characteristics with areas with diverse catchments exhibiting lower levels of dependence.