The production of φ mesons in the reaction e+p → e+φp (gf → K+K−) at a median Q2 of 10−4 GeV2 h been studied with the ZEUS detector at HERA. The differential φ photoproduction cross section 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 sect σγp→φp = 0.96±0.19−0.18+0.21μb 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.