Measurements of the cross sections for charged current deep inelastic scattering in e(-)p collisions with longitudinally polarised electron beams are presented. The measurements are based on a data sample with an integrated luminosity of 175 pb(-1) collected with the ZEUS detector at HERA at a centre-of-mass energy of 318 GeV. The total cross section is given for positively and negatively polarised electron beams. The differential cross-sections d sigma/dQ(2), d sigma/dx and d sigma/dy are presented for Q(2) > 200 GeV2. The double-differential cross-section d(2)sigma/dxdQ(2) is presented in the kinematic range 280 < Q(2) < 30 000 GeV2 and 0.015 < x < 0.65. The measured cross sections are compared with the predictions of the Standard Model.