A search is presented for the pair-production of heavy vector-like quarks in the lepton+jets final state using 140 fb−1 of proton–proton collisions at s=13 TeV collected with the ATLAS detector. The search is optimised for vector-like top-quarks (T) that decay into a W boson and a b-quark, with one W boson decaying leptonically and the other hadronically. Other vector-like quark flavours and decay modes are also considered. Events are selected with one high transverse-momentum electron or muon, large missing transverse momentum, a large-radius jet identified as a W boson, and multiple small-radius jets, at least one of which is b-tagged. Vector-like T-quarks with 100% branching ratio to Wb are excluded at 95% CL for masses below 1700 GeV. These limits are also applied to vector-like Y-quarks, which decay exclusively into a W boson and a b-quark. Isospin singlets with B(T→Wb:Ht:Zt)=1/2:1/4:1/4 are excluded for masses below 1360 GeV.