The photoproduction of D * ± mesons has been measured with the ZEUS detector at HERA at three different ep centre-of-mass energies, √ s, of 318, 251 and 225 GeV. For each data set, D * ± mesons were required to have transverse momentum, p D * T , and pseudorapidity, η D * , in the ranges 1.9 < p D * T < 20 GeV and |η D * | < 1.6. The events were required to have a virtuality of the incoming photon, Q 2 , of less than 1 GeV 2 . The dependence on √ s was studied by normalising to the high-statistics measurement at √ s = 318 GeV.This led to the cancellation of a number of systematic effects both in data and theory.Predictions from next-to-leading-order QCD describe the √ s dependence of the data well.