A search for single production of a vector-like quark $Q$, which could be either a singlet $T$, with charge $\tfrac23$, or a $Y$ from a $(T,B,Y)$ triplet, with charge $-\tfrac43$, is performed using data from proton-proton collisions at a centre-of-mass energy of 13 TeV. The data correspond to the full integrated luminosity of 140 fb$^{-1}$ recorded with the ATLAS detector during Run 2 of the Large Hadron Collider. The analysis targets $Q \to Wb$ decays where the $W$ boson decays leptonically. The data are found to be consistent with the expected Standard Model background, so upper limits are set on the cross-section times branching ratio, and on the coupling of the $Q$ to the Standard Model sector for these two benchmark models. Effects of interference with the Standard Model background are taken into account. For the singlet $T$, the 95% confidence level limit on the coupling strength $κ$ ranges between 0.22 and 0.52 for masses from 1150 to 2300 GeV. For the $(T,B,Y)$ triplet, the limits on $κ$ vary from 0.14 to 0.46 for masses from 1150 to 2600 GeV.
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