A search for singly produced vector-like quarks Q, where Q can be either a T quark with charge +2/3 or a Y quark with charge −4/3, is performed in proton–proton collision data at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 36.1 fb−1, recorded with the ATLAS detector at the LHC in 2015 and 2016. The analysis targets Q → Wb decays where the W boson decays leptonically. No significant deviation from the expected Standard Model background is observed. Upper limits are set on the QWb coupling strength and the mixing between the Standard Model sector and a singlet T quark or a Y quark from a (B, Y) doublet or a (T, B, Y) triplet, taking into account the interference effects with the Standard Model background. The upper limits set on the mixing angle are as small as |sin θL| = 0.18 for a singlet T quark of mass 800 GeV, |sin θR| = 0.17 for a Y quark of mass 800 GeV in a (B, Y) doublet model and |sin θL| = 0.16 for a Y quark of mass 800 GeV in a (T, B, Y) triplet model. Within a (B, Y) doublet model, the limits set on the mixing parameter |sin θR| are comparable with the exclusion limits from electroweak precision observables in the mass range between about 900 GeV and 1250 GeV.[Figure not available: see fulltext.]