The life history characteristics of some elasmobranchs make them particularly vulnerable to fishing mortality; about a third of all species are listed by the IUCN as Threatened or Near Threatened. Marine Protected Areas (MPAs) have been suggested as a tool for conservation of elasmobranchs, but they are likely to be effective only if such populations respond to fishing impacts at spatial-scales corresponding to MPA size. Using the example of the Celtic Sea, we modelled elasmobranch biomass (kg h−1) in fisheries-independent survey hauls as a function of environmental variables and ‘local’ (within 20 km radius) fishing effort (h y−1) recorded from Vessel Monitoring Systems data. Model selection using AIC suggested strongest support for linear mixed effects models in which the variables (i) fishing effort, (ii) geographic location and (iii) demersal fish assemblage had approximately equal importance in explaining elasmobranch biomass. In the eastern Celtic Sea, sampling sites that occurred in the lowest 10% of the observed fishing effort range recorded 10 species of elasmobranch including the critically endangered Dipturus spp. The most intensely fished 10% of sites had only three elasmobranch species, with two IUCN listed as Least Concern. Our results suggest that stable spatial heterogeneity in fishing effort creates de facto refugia for elasmobranchs in the Celtic Sea. However, changes in the present fisheries management regime could impair the refuge effect by changing fisher's behaviour and displacing effort into these areas.