Inclusive-jet cross sections have been measured in the reaction ep -> e + jet + X for photon virtuality Q(2) < 1 GeV2 and gamma p centre-of-mass energies in the region 142 < W-gamma p < 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-T(jet), and pseudorapidity, eta(jet), for jets with E-T(jet) > 17 GeV and -1 < eta(jet) < 2.5. In addition, measurements of double-differential inclusive-jet cross sections are presented as functions of E-T(jet) in different regions of eta(jet). Next-to-leading-order QCD calculations give a good description of the measurements, except for jets with low E-T(jet) and high eta(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(alpha(2)(s)) terms. Values of alpha s (M-Z) were extracted from the measurements and the energy-scale dependence of the coupling was determined. The value of alpha(s) (M-Z) extracted from the measurements based on the k(T) jet algorithm is alpha(s) (M-Z) = 0.1206(-0.0022)(+0.0023)(exp.)(-0.0035)(+0.0042)(th.); the results from the anti-k(T) and SIScone algorithms are compatible with this value and have a similar precision.