We consider tracer diffusion in colloidal suspensions under solid loading conditions, where hydrodynamic interactions play an important role. To this end, we carry out computer simulations based on the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) technique. Many details of the simulation method are discussed in detail. In particular, our choices for the SRD-MD parameters and for the different scales are adapted to simulating colloidal suspensions under realistic conditions. Our simulation data are compared with published theoretical, experimental and numerical results and compared to Brownian dynamics simulation data. We demonstrate that our SRD-MD simulations reproduce many features of the hydrodynamics in colloidal fluids under finite loading. In particular, finite-size effects and the diffusive behavior of colloids for a range of volume fractions of the suspension show that hydrodynamic interactions are correctly included within the SRD-MD technique.