A search is presented for the production of a single top quark via left-handed flavour-changing neutral-current (FCNC) interactions of a top quark, a gluon and an up or charm quark. Two production processes are considered: $$u+g\rightarrow t$$ u + g → t and $$c+g\rightarrow t$$ c + g → t . The analysis is based on proton–proton collision data taken at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. The data set corresponds to an integrated luminosity of 139 fb$$^{-1}$$ - 1 . Events with exactly one electron or muon, exactly one b-tagged jet and missing transverse momentum are selected, resembling the decay products of a singly produced top quark. Neural networks based on kinematic variables differentiate between events from the two signal processes and events from background processes. The measured data are consistent with the background-only hypothesis, and limits are set on the production cross-sections of the signal processes: $$\sigma (u+g\rightarrow t)\times \mathcal {B}(t\rightarrow Wb)\times \mathcal {B}(W\rightarrow \ell \nu )