The inclusive $t\bar{t}$ production cross-section is 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-based approach. The inclusive $t\bar{t}$ cross-section is measured with a precision of 5.7% to be $\sigma_{t\bar{t}} = 248.3 \pm 0.7 \, (\mathrm{stat.}) \pm 13.4 \, (\mathrm{syst.}) \pm 4.7 \, (\mathrm{lumi.})~\text{pb}$, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction.