The results of a search for new heavy W′ bosons decaying to an electron or muon and a neutrino using proton–proton collision data at a centre-of-mass energy of √s=13 TeV are presented. The dataset was collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider and corresponds to an integrated luminosity of 36.1 fb⁻¹. As no excess of events above the Standard Model prediction is observed, the results are used to set upper limits on the W′ boson cross-section times branching ratio to an electron or muon and a neutrino as a function of the W′ mass. Assuming a W′ boson with the same couplings as the Standard Model W boson, W′ masses below 5.1 TeV are excluded at the 95% confidence level.