Diffusion of vacancies and impurities in metals is important in many processes occurring in structural materials. This diffusion often takes place in the presence of spatially rapidly varying stresses. Diffusion under stress is frequently modelled by local approximations to the vacancy formation and diffusion activation enthalpies which are linear in the stress, in order to account for its dependence on the local stress state and its gradient. Here, more accurate local approximations to the vacancy formation and diffusion activation enthalpies, and the simulation methods needed to implement them, are introduced. The accuracy of both these approximations and the linear approximations are assessed via comparison to full atomistic studies for the problem of vacancies around a Lomer dislocation in Aluminium. Results show that the local and linear approximations for the vacancy formation enthalpy and diffusion activation enthalpy are accurate to within 0.05 eV outside a radius of about 13 Angstrom (local) and 17 Angstrom (linear) from the centre of the dislocation core or, more generally, for a strain gradient of roughly up to 6 x 10(6) m(-1) and 3 x 10(6) m(-1), respectively. These results provide a basis for the development of multiscale models of diffusion under highly non-uniform stress.