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 dσ/dQ2, dσ/dx and dσ/dy are presented for Q2>200 GeV2. The double-differential cross-section d2σ/dxdQ2 is presented in the kinematic range 280<Q2<30 000 GeV2 and 0.015<x<0.65. The measured cross sections are compared with the predictions of the Standard Model.