We evaluate the performance of different van der Waals (vdW) corrected density functional theory (DFT) methods in predicting the structure of perfect interfaces between the LiF(001), MgO(001), NiO(001) films on the Ag(001) surface and the resulting work function shift of Ag(001). The results demonstrate that including the van der Waals interaction is important for obtaining accurate interface structures and the metal work function shift. The work function shift results from a subtle interplay of several effects strongly affected by even small changes in the interface geometry. This makes the accuracy of theoretical methods insufficient for predicting the shift values better than within 0.2 eV. Most of the existing van der Waals corrected functionals are not particularly suited for studying metal/insulator interfaces. The lack of accurate experimental data on the interface geometries and surface rumpling of insulators hampers the calibration of existing and novel density functionals.