Measurement of deep inelastic inclusive and diffractive scattering with Q2 between 25 and 320 GeV2 with the ZEUS Forward Plug Calorimeter at HERA Deep inelastic scattering and its diffractive component, ep -> e'gamma*p -> e'XN, was studied with the ZEUS detector at HERA using an integrated luminosity of 52.4 pb-1. The M_X method was used to extract the diffractive contribution. A wide range of the centre-of-mass energy W (37 - 245GeV), photon virtuality Q2 (20 - 450 GeV2) and mass M_X (0.28 - 35 GeV) is covered. The diffractive cross section for 2 < M_X < 15 GeV rises strongly with W, the rise becoming steeper as Q2 increases. The data are also presented in terms of the diffractive structure function, F^D(3)_2, of the proton. For fixed Q2 and fixed M_X, x_IP F^D(3)_2 shows a strong rise as x_IP -> 0, where x_IP is the fraction of the proton momentum carried by the Pomeron. For Bjorken-x < 10^{-3}, x_IP F^D(3)_2 shows positive log Q2 scaling violations, while for x > 5 10^-3 negative scaling violations are observed. The diffractive structure function is compatible with being leading twist. The data show that Regge factorisation is broken.