ABSTRACT The WALLABY pilot survey has been conducted using the Australian SKA Pathfinder (ASKAP). The integrated 21-cm H i line spectra are formed in a very different manner compared to usual single-dish spectra Tully–Fisher measurements. It is thus extremely important to ensure that slight differences (e.g. biases due to missing flux) are quantified and understood in order to maximise the use of the large amount of data becoming available soon. This article is based on four fields for which the data are scientifically interesting by themselves. The pilot data discussed here consist of 614 galaxy spectra at a rest wavelength of 21 cm. Of these spectra, 472 are of high enough quality to be used to potentially derive distances using the Tully–Fisher relation. We further restrict the sample to the 251 galaxies whose inclination is sufficiently close to edge-on. For these, we derive Tully–Fisher distances using the deprojected WALLABY velocity widths combined with infrared (WISE W1) magnitudes. The resulting Tully–Fisher distances for the Eridanus, Hydra, Norma, and NGC4636 clusters are 21.5, 53.5, 69.4, and 23.0 Mpc, respectively, with uncertainties of 5–10 per cent, which are better or equivalent to the ones obtained in studies using data obtained with giant single dish telescopes. The pilot survey data show the benefits of WALLABY over previous giant single-dish telescope surveys. WALLABY is expected to detect around half a million galaxies with a mean redshift of $z = 0.05 (200\, \mathrm{Mpc})$. This study suggests that about 200 000 Tully–Fisher distances might result from the survey.