The inclusive and fiducial t (t) over bar production cross sections are measured in the lepton+jets channel using 20.2 fb(-1) of proton proton collision data at a centre-of mass energy of 8 TeV recorded with the ATLAS detector at the LHC. Major systematic uncertainties due to the modelling of the jet energy scale and b-tagging efficiency are constrained by separating selected events into three disjoint regions. In order to reduce systematic uncertainties in the most important background, the W+jets process is modelled using Z+jets events in a data-driven approach. The inclusive t (t) over bar cross-section is measured with a precision of 5.7% to be (sigma(inc) (t (t) over bar) = 248.3 +/- 0.7 (stat.) +/- 13.4 (syst.) +/- 4.7 (lumi.) pb, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction. The cross-section is also measured in a phase space close to that of the selected data. The fiducial cross-section is sigma(fid) (t (t) over bar) = 48.8 +/- 0.1 (stat.) +/- 2.0 (syst.) +/- 0.9 (lumi.) pb with a precision of 4.5%.