A search is presented for the pair production of heavy vector-like B quarks, primarily targeting B quark decays into a W boson and a top quark. The search is based on 36.1 fb−1 of pp collisions at √s=13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, characterised by a high-transverse-momentum isolated electron or muon, large missing transverse momentum, and multiple jets, of which at least one is b-tagged. No significant deviation from the Standard Model expectation is observed. The 95% confidence level lower limit on the B mass is 1350 GeV assuming a 100% branching ratio to Wt. In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. The 100% branching ratio limits are found to be also applicable to heavy vector-like X production, with charge +5/3, that decay into Wt. This search is also sensitive to a heavy vector-like B quark decaying into other final states (Zb and Hb) and thus mass limits on B production are set as a function of the decay branching ratios.