The inclusive e(-)p single and double differential cross sections for neutral and charged current processes are measured with the H1 detector at HERA, in the range of four-momentum transfer squared Q(2) between 150 and 30 000 GeV2, and Bjorken x between 0.002 and 0.65. The data were taken in 1998 and 1999 with a centre-of-mass energy of 320 GeV and correspond to an integrated luminosity of 16.4 pb(-1) The data are compared with recent measurements of the inclusive neutral and charged current e(+)p cross sections. For Q(2) > 1000 GeV2 clear evidence is observed for an asymmetry between e(+)p and e(-)p neutral current scattering and the generalised structure functions x (F) over tilde (3) is extracted for the first time at HERA. A fit to the charged current data is used to extract a value for the W boson propagator mass. The data are found to be in good agreement with Standard Model predictions.