The diffractive process ep → eXY , where Y denotes a proton or its low mass excitation with M Y < 1.6 GeV, is studied with the H1 experiment at HERA. The analysis is restricted to the phase space region of the photon virtuality 3 ≤ Q 2 ≤ 1600 GeV 2 , the square of the fourmomentum transfer at the proton vertex |t| < 1. Triple differential cross sections are measured as a function of x P , Q 2 and β = x/x P where x is the Bjorken scaling variable. These measurements are made after selecting diffractive events by demanding a large empty rapidity interval separating the final state hadronic systems X and Y . large rapidity gap selection method. The combined data represent a factor between three and thirty increase in statistics with respect to the previously published results. The measurements are compared with predictions from NLO QCD calculations based on diffractive parton densities and from a dipole model. The proton vertex factorisation hypothesis is tested.