The electronic properties of Tm and Lu atoms adsorbed on nanoscale Cu2N insulating islands and on a clean Cu(100) surface have been investigated by scanning tunnelling microscopy and spectroscopy, and density functional calculations modelling the electronic structure of the rare earth atoms were performed. While Lu adatoms display the same spectra on both surfaces, tunnelling spectra of Tm on Cu2N indicate a state at ≃0.8 V or ≃1.9 V bias, depending on the 4f population of the adatom, 4f12 or 4f13, which is not present on Tm atoms adsorbed on Cu(100). Although inelastic 4f-spin-flip excitations were not detected, variation of tunnelling through the strongly correlated d-electrons indicates that the insulating layer opens a pathway to access the electronic state of those 4f electrons in the single adatom.