The diffractive process ep→eXY, where Y denotes a proton or its low mass excitation with MY<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 ≤ Q2 ≤ 1600 GeV2, the square of the four-momentum transfer at the proton vertex {pipe}t{pipe}< 1.0 GeV2 and the longitudinal momentum fraction of the incident proton carried by the colourless exchange xℙ<0.05. Triple differential cross sections are measured as a function of xℙ, Q2 and β=x/xℙ 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. High statistics measurements covering the data taking periods 1999-2000 and 2004-2007 are combined with previously published results in order to provide a single set of diffractive cross sections from the H1 experiment using the 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. © 2012 The Author(s).