Follow-up observations of large numbers of gamma-ray burst (GRB) afterglows, facilitated by the Swift satellite, have produced a large sample of spectral energy distributions and light curves, from which their basic micro- and macro-physical parameters can in principle be derived. However, a number of phenomena have been observed that defy explanation by simple versions of the standard fireball model, leading to a variety of new models. Polarimetry can be a major independent diagnostic of afterglow physics, probing the magnetic field properties and internal structure of the GRB jets. In this paper we present the first high-quality multi-night polarimetric light curve of a Swift GRB afterglow, aimed at providing a well-calibrated data set of a typical afterglow to serve as a benchmark system for modelling afterglow polarization behaviour. In particular, our data set of the afterglow of GRB 091018 (at redshift z = 0.971) comprises optical linear polarimetry (R band, 0.13–2.3 d after burst); circular polarimetry (R band) and near-infrared linear polarimetry (Ks band). We add to that high-quality optical and near-infrared broad-band light curves and spectral energy distributions as well as afterglow spectroscopy. The linear polarization varies between 0 and 3 per cent, with both long and short time-scale variability visible. We find an achromatic break in the afterglow light curve, which corresponds to features in the polarimetric curve. We find that the data can be reproduced by jet break models only if an additional polarized component of unknown nature is present in the polarimetric curve. We probe the ordered magnetic field component in the afterglow through our deep circular polarimetry, finding Pcirc < 0.15 per cent (2σ), the deepest limit yet for a GRB afterglow, suggesting ordered fields are weak, if at all present. Our simultaneous R- and Ks-band polarimetry shows that dust-induced polarization in the host galaxy is likely negligible.