Measurement of high-Q2 charged current deep inelastic e-p scattering cross sections with longitudinally polarised electrons with ZEUS at HERA Measurements of the cross sections for charged current deep inelastic scattering in e-p collisions with a longitudinally polarised electron beam are presented. The measurements are based on a data sample with an integrated luminosity of 174 pb-1 collected with the ZEUS detector at HERA from 2004 to 2006 at a centre-of-mass energy of 318 GeV. The total cross section is presented at positive and negative values of the longitudinal polarisation of the electron beam. A fit to these measurements yields an upper limit on the right-handed charged current cross section of 4.8 pb and a lower limit on the mass of a right-handed W boson of 400 GeV. The differential cross sections d#/dQ2,d#/dx and d#/dy for Q2>200 GeV2 are presented. In addition d2#/dxdQ2 was measured in the kinematic range 280 GeV2 < Q2 < 30000 GeV2 and 0.015 < x < 0.65. The measured cross sections are compared with the predictions of the Standard Model. An electroweak analysis of the measurements yields a value of 79.4 (+1.7/-1.5) GeV for the mass of the W boson.