The cross-section for inelastic proton-proton collisions, with at least one prompt long-lived charged particle of transverse momentum p T > 0.2GeV/c in the pseudorapidity range 2.0 < η < 4.5, is measured by the LHCb experiment at a centre-of-mass energy of s√ = 7 TeV. The cross-section in this kinematic range is determined to be σ accinel = 55.0 ± 2.4 mb with an experimental uncertainty that is dominated by systematic contributions. Extrapolation to the full phase space, using Pythia 6, yields σ inel = 66.9 ± 2.9 ± 4.4 mb, where the first uncertainty is experimental and the second is due to the extrapolation.