In this work we propose a general strategy to calculate accurate He–surface interaction potentials. It extends the dispersionless density functional approach recently developed by Pernal et al. [Phys. Rev. Lett.103, 263201 (2009)] to adsorbate-surface interactions by including periodic boundary conditions. We also introduce a scheme to parametrize the dispersion interaction by calculating two- and three-body dispersion terms at coupled cluster singles and doubles and perturbative triples (CCSD(T)) level via the method of increments [H. Stoll, J. Chem. Phys.97, 8449 (1992)]. The performance of the composite approach is tested on 4He/graphene by determining the energies of the low-lying selective adsorption states, finding an excellent agreement with the best available theoretical data. Second, the capability of the approach to describe dispersionless correlation effects realistically is used to extract dispersion effects in time-dependent density functional simulations on the collision of 4He droplets with a single graphene sheet. It is found that dispersion effects play a key role in the fast spreading of the 4He nanodroplet, the evaporation-like process of helium atoms, and the formation of solid-like helium structures. These characteristics are expected to be quite general and highly relevant to explain experimental measurements with the newly developed helium droplet mediated deposition technique.