The top anti-top quark production cross-section is measured in the lepton+jets channel using proton-proton collision data at a centre-of-mass energy of root s = 13 TeV collected with the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 139 fb(-1). Events with exactly one charged lepton and four or more jets in the final state, with at least one jet containing b-hadrons, are used to determine the a production cross-section through a profile-likelihood t (t) over bar. The inclusive cross-section is measured to be alpha(inc) = 830 +/- 0.4 (stat.) +/- 36 (syst.) +/- 14 (lumi.) pb with a relative uncertainty of 4.6%. The result is consistent with theoretical calculations at next-to-next-to-leading order in perturbative QCD. The fiducial t (t) over bar cross-section within the experimental acceptance is also measured.