Inclusive e(+/-)p single and double differential cross sections for neutral and charged current deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of root s = 319 GeV with a total integrated luminosity of 333.7 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, Q(2), between 60 and 50 000GeV(2), 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 xF(3)(gamma Z). A measurement of the neutral current parity violating structure function F-2(gamma Z) is presented for the first time. The polarisation dependence of the charged current total cross section is also measured. The new measurements are 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.