Inclusive ep single and double differential cross sections for neutral (NC) and charged current (CC) deep inelastic scattering processes are measured with the H1 detector at HERA. The datawere taken at a centre-of-mass energy of sqrt(s) = 319 GeV with a total integrated luminosity of 327.8 pb-1 shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative four-momentum transfer squared, Q2, between 60 and 50 000 GeV2, and Bjorken x between 0.0008 and 0.65. The measurements are combined with earlier published unpolarised H1 data to improve statistical precision and used to determine the structure function xFgammaZ3. A measurement of the structure function FgammaZ2, sensitive to parity violating effects in NC, is presented for the first time. The polarisation dependence of the CC total cross section is also measured. The new measurementsare well described by a next-to-leading order QCD fit based on all published H1 inclusive cross section data which are used to extract the parton distribution functions of the proton.