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Inclusive-jet cross sections have been measured in the reaction ep → e + jet + X for photon virtuality Q 2 < 1 GeV 2 and γp centre-of-mass energies in the region 142 < W γp < 293 GeV with the ZEUS detector at HERA using an integrated luminosity of 300 pb −1 . Jets were identified using the k T , anti-k T or SIScone jet algorithms in the laboratory frame. Single-differential cross sections are presented as functions of the jet transverse energy, E jet T , and pseudorapidity, η jet , for jets with E jet T > 17 GeV and −1 < η jet < 2.5. In addition, measurements of double-differential inclusive-jet cross sections are presented as functions of E jet T in different regions of η jet . Next-to-leading-order QCD calculations give a good description of the measurements, except for jets with low E jet T and high η jet . The influence of non-perturbative effects not related to hadronisation was studied. Measurements of the ratios of cross sections using different jet algorithms are also presented; the measured ratios are well described by calculations including up to O(α