The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We use the very forward neutron energy spectra measured by the LHC forward experiment at 7 TeV to extract the π þ p total cross section at center-of-mass energies in the range 2.3-3.5 TeV. To do this, we have to first isolate the π-exchange pole in forward neutron production in pp collisions, by evaluating other possible contributions, namely, those from ρ and a 2 exchange, from both eikonal and enhanced screening effects, from migration, from neutron production by Δ-isobar decay and from diffractive nucleon excitations. We discuss the possible theoretical uncertainties due to the fact that the data do not exactly reach the π pole. We choose the kinematical domain where the pion contribution dominates and demonstrate the role of the different corrections which could affect the final result.