Measurements of the neutral current cross sections for deep inelastic scattering in e - p collisions at HERA with a longitudinally polarised electron beam are presented. The single-differential cross-sections d σ/dQ 2, d σ/dx and d σ/dy and the double-differential cross sections in Q 2 and x are measured in the kinematic region y185∈GeV 2 for both positively and negatively polarised electron beams and for each polarisation state separately. The measurements are based on an integrated luminosity of 169.9∈pb -1 taken with the ZEUS detector in 2005 and 2006 at a centre-of-mass energy of 318∈GeV. The structure functions F3 and xF 3γ Z are determined by combining the e - p results presented in this paper with previously measured e + p neutral current data. The asymmetry parameter A - is used to demonstrate the parity violating effects of electroweak interactions at large spacelike photon virtuality. The measurements agree well with the predictions of the Standard Model. © 2009 Springer-Verlag / Società Italiana di Fisica.