The production of φ mesons in the reaction e+p → e+φp (φ → K+K-) at a median Q2 of 10-4 GeV2 has been studied with the ZEUS detector at HERA. The differential φ photoproduction cross section dσ/dt has an exponential shape and has been determined in the kinematic range 0.1 < |t| < 0.5 GeV2 and 60 < W < 80 GeV. An integrated cross section of σγp→φp = 0.96 ± 0.19+0.21-.18 μb has been obtained by extrapolating to t = 0. When compared to lower energy data, the results show a weak energy dependence of both σγp→φp and the slope of the t distribution. The φ decay angular distributions are consistent with s-channel helicity conservation. From lower energies to HERA energies, the features of φ photoproduction are compatible with those of a soft diffractive process.