We present a homogeneous, high signal‐to‐noise spectropolarimetric survey of 16 northern hemisphere Wolf–Rayet (WR) stars. A reduction in polarization at emission‐line wavelengths — the ‘line effect’— is identified in four stars: WRs 134, 137, 139, and 141. The magnitude of the effect in WR 139 (V444 Cyg) is variable, while WR 136, previously reported to show the line effect, does not show it in our data. Assuming the line effect generally to arise from axisymmetric distortions of stellar winds, we show that a model in which all WRs have the same intrinsic (equator‐on) polarization, with the observed variations solely a result of inclination effects, is inconsistent with the observations. A model in which the intrinsic polarizations are uniformly distributed is more plausible, but best‐fitting results are obtained if the distribution of polarizations is biased towards small values, with only ∼ 20 per cent of stars having intrinsic polarizations greater than ∼ 0.3 per cent. Radiative transfer calculations indicate that the observed continuum polarizations can be matched by models with equator:pole density ratios of 2–3. The model spectra have electron‐scattering wings that are significantly stronger than observed (in both intensity and polarized flux), confirming that the winds of stars showing intrinsic polarization must be clumped on small scales as well as being distorted on large scales. We combine the results of our survey with observations from the literature to give a sample of 29 stars which have both accurate spectropolarimetric observations and physical parameters derived from standard‐model analyses. We find that the line‐effect stars are clustered at high M, L in the luminosity–mass‐loss rate plane (although they are unexceptional in the terminal velocity–subtype and the surface‐mass‐flux–temperature planes). The mass‐loss rates derived from radio‐continuum observations for these stars are in good accord with the results of optical emission‐line analyses, suggesting that (i) the wind structure of line‐effect stars has a density contrast which is effectively constant with radius, and (ii) the high M values may be artefacts of large‐scale wind structure. Assuming that observed spectroscopic and photometric variability of the line‐effect stars is related to the WR rotation period, we compute equatorial rotation velocities. These velocities correspond to ∼ 10 per cent of the core breakup rates, and may be large enough to produce significant wind‐compression effects according to the models of Ignace, Cassinelli & Bjorkman.