We present the results of a programme of thermal‐infrared imaging of 19 z∼ 1 radio galaxies from the 3CR and 3CRR (LRL) samples. We detect emission at L′ (3.8 μm) from four objects; in each case the emission is unresolved at 1‐arcsec resolution. 15 radio galaxies remain undetected to sensitive limits of L′≈ 15.5. Using these data in tandem with archived HST data and near‐infrared spectroscopy, we show that three of the detected ‘radio galaxies’ (3C 22, 3C 41 and 3C 65) harbour quasars reddened by AV≲ 5 mag. Correcting for this reddening, 3C 22 and 3C 41 are very similar to coeval 3C quasars, whilst 3C 65 seems unusually underluminous. The fourth radio galaxy detection (3C 265) is a more highly obscured (AV∼ 15) but otherwise typical quasar, which previously has been evident only in scattered light. We determine the fraction of dust‐reddened quasars at z∼ 1 to be 28−13+25 per cent at 90 per cent confidence. On the assumption that the undetected radio galaxies harbour quasars similar to those in 3C 22, 3C 41 and 3C 265 (as seems reasonable, given their similar narrow emission line luminosities) we deduce extinctions of AV≳: 15 towards their nuclei. The contributions of reddened quasar nuclei to the total K‐band light range from ∼0 per cent for the non‐detections, through ∼10 per cent for 3C 265 to ∼80 per cent for 3C 22 and 3C 41. Correcting for these effects does not remove the previously reported differences between the K magnitudes of 3C and 6C radio galaxies, so contamination by reddened quasar nuclei is not a serious problem for drawing cosmological conclusions from the K–z relation for radio galaxies. We discuss these results in the context of the ‘receding torus’ model which predicts a small fraction of lightly reddened quasars in samples of high‐radio‐luminosity sources. We also examine the likely future importance of thermal‐infrared imaging in the study of distant powerful radio sources.