This paper presents a measurement of the top quark pair t t ¯ production charge asymmetry A C using 4.7 fb −1 of proton-proton collisions at a centre-of-mass energy √s = 7 TeV collected by the ATLAS detector at the LHC. A $ t\overline{t} $ -enriched sample of events with a single lepton (electron or muon), missing transverse momentum and at least four high transverse momentum jets, of which at least one is tagged as coming from a b -quark, is selected. A likelihood fit is used to reconstruct the $ t\overline{t} $ event kinematics. A Bayesian unfolding procedure is employed to estimate A C at the parton-level. The measured value of the $ t\overline{t} $ production charge asymmetry is A C = 0.006 ± 0.010, where the uncertainty includes both the statistical and the systematic components. Differential A C measurements as a function of the invariant mass, the rapidity and the transverse momentum of the $ t\overline{t} $ system are also presented. In addition, A C is measured for a subset of events with large t t ¯ velocity, where physics beyond the Standard Model could contribute. All measurements are consistent with the Standard Model predictions.