The diffractive photoproduction of ρ mesons, e p → e ρ Y, with large momentum transfer squared at the proton vertex, |t|, is studied with the H1 detector at HERA using an integrated luminosity of 20.1   pb-1. The photon-proton centre of mass energy spans the range 75 < W < 95   GeV, the photon virtuality is restricted to Q2 < 0.01   GeV2 and the mass MY of the proton remnant is below 5 GeV. The t dependence of the cross section is measured for the range 1.5 < | t | < 10.0   GeV2 and is well described by a power law, d σ / d | t | ∝ | t |- n. The spin density matrix elements, which provide information on the helicity structure of the interaction, are extracted using measurements of angular distributions of the ρ decay products. The data indicate a violation of s-channel helicity conservation, with contributions from both single and double helicity-flip being observed. The results are compared to the predictions of perturbative QCD models. © 2006 Elsevier B.V. All rights reserved.