Measurement of high-Q2 neutral current deep inelastic e-p scattering cross sections with longitudinally polarised electrons in ZEUS at HERA Measurements of the neutral current cross sections for deep inelastic scattering in e-p collisions at HERA with longitudinally polarised electron beams are presented. Single differential cross sections in Q2, x and y, and double differential cross sections in Q2 and x are shown in the kinematic region of Q2 > 185 GeV separately for positively and negatively polarised electrons. The measurements are based on an integrated luminosity of 177 pb-1 collected by the ZEUS detector from 2005 to 2006 with a centre-of-mass energy of 318 GeV. The structure function xF3 is measured by combining the e-p data presented in this paper with previously measured unpolarised e+p neutral current data. The asymmetry parameter A- is used to demonstrate the parity violating effects of electroweak interactions. The Standard Model agrees well with all measurements.