Measurements of the cross sections for charged current deep inelastic scattering in e (+) p collisions with a longitudinally polarised positron beam are presented. The measurements are based on a data sample with an integrated luminosity of 132 pb(-1) collected with the ZEUS detector at HERA 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 positron beams. The single-differential cross-sections d sigma/dQ (2), d sigma/dx and d sigma/dy are presented for Q (2)> 200 GeV2. The reduced cross-section is presented in the kinematic range 200 < Q (2)< 60 000 GeV2 and 0.006 < x < 0.562. The measurements agree well with the predictions of the Standard Model. The results are used to determine a lower limit on the mass of a hypothetical right-handed W boson.