Polycrystalline recrystallized tungsten samples were irradiated with 7.5 MeV Si ions and 9 MeV Cu ions to three different damage levels (0.01, 0.1, 0.5 dpa at 200 nm depth) at 295 K. The resulting vacancy-type defects in the samples were studied using positron annihilation lifetime spectroscopy. The dependence of the average positron lifetime on the damage level is found to be non-linear: a steep increase at low damage levels with a tendency to saturation at higher damage levels (>0.1 dpa). The average positron lifetime of Si and Cu-irradiated tungsten is very similar at each damage level, suggesting similar vacancy-type defect structure. Deconvolution of the positron lifetime spectra revealed that the dominant irradiation-induced defect type is a single vacancy. The presence of small vacancy clusters is also detected. Their fraction is found to increase with increasing damage level.