We study the 37 brightest radio sources in the Subaru/XMM-Newton Deep Field. We have spectroscopic redshifts for 24 of 37 objects and photometric redshifts for the remainder, yielding a median redshift z med for the whole sample of z med≃ 1.1 and a median radio luminosity close to the 'Fanaroff-Riley type I/type II (FR I/FR II)' luminosity divide. Using mid-infrared (mid-IR) (Spitzer MIPS 24 μm) data we expect to trace nuclear accretion activity, even if it is obscured at optical wavelengths, unless the obscuring column is extreme. Our results suggest that above the FR I/FR II radio luminosity break most of the radio sources are associated with objects that have excess mid-IR emission, only some of which are broad-line objects, although there is one clear low-accretion-rate object with an FR I radio structure. For extended steep-spectrum radio sources, the fraction of objects with mid-IR excess drops dramatically below the FR I/FR II luminosity break, although there exists at least one high-accretion-rate 'radio-quiet' QSO. We have therefore shown that the strong link between radio luminosity (or radio structure) and accretion properties, well known at z∼ 0.1, persists to z∼ 1. Investigation of mid-IR and blue excesses shows that they are correlated as predicted by a model in which, when significant accretion exists, a torus of dust absorbs ∼30 per cent of the light, and the dust above and below the torus scatters ≳1 per cent of the light.