•Topological Hall effect found in Pt/Co/W multilayers with different signs of anisotropy.•Negative topological Hall contribution due to nucleated isolated skyrmions.•Positive topological Hall contribution isolated non-annihilated skyrmions.•Skyrmion numbers of complex domain structures reproduced micromagmetically. The chirality of non-coplanar magnetic configurations, in magnetic materials with interfacial Dzyaloshinskii–Moriya interaction, gives rise to a local magnetic field generating an extra contribution to the anomalous Hall effect. This contribution, termed topological Hall effect (THE), is studied in three Pt/Co/W multi-layered samples with different effective anisotropy. A particularity of this system, compared to similar systems which show THE, is the existence of magnetically inactive layers at the Co/W interfaces. This implies that the coupling between the layers in this series of samples is mainly magnetostatic. The samples with positive or almost zero effective anisotropy show the same characteristics. These are reproduced by micromagnetic simulations. The sample with negative effective anisotropy shows a qualitatively different behaviour that can be assigned to its radically different domain structure. The values of THE are in the range 0.1–0.25 μΩ cm.