Identifying and quantifying the effects of climate change that alter the habitat overlap of marine predators and their prey population distributions is of great importance for the sustainable management of populations. This study uses Bayesian joint models with integrated nested Laplace approximation (INLA) to predict future spatial density distributions in the form of common spatial trends of predator–prey overlap in 2050 under the “business‐as‐usual, worst‐case” climate change scenario. This was done for combinations of six mobile marine predator species (gray seal, harbor seal, harbor porpoise, common guillemot, black‐legged kittiwake, and northern gannet) and two of their common prey species (herring and sandeels). A range of five explanatory variables that cover both physical and biological aspects of critical marine habitat were used as follows: bottom temperature, stratification, depth‐averaged speed, net primary production, and maximum subsurface chlorophyll. Four different methods were explored to quantify relative ecological cost/benefits of climate change to the common spatial trends of predator–prey density distributions. All but one future joint model showed significant decreases in overall spatial percentage change. The most dramatic loss in predator–prey population overlap was shown by harbor seals with large declines in the common spatial trend for both prey species. On the positive side, both gannets and guillemots are projected to have localized regions with increased overlap with sandeels. Most joint predator–prey models showed large changes in centroid location, however the direction of change in centroids was not simply northwards, but mostly ranged from northwest to northeast. This approach can be very useful in informing the design of spatial management policies under climate change by using the potential differences in ecological costs to weigh up the trade‐offs in decisions involving issues of large‐scale spatial use of our oceans, such as marine protected areas, commercial fishing, and large‐scale marine renewable developments.