A search for a light charged Higgs boson produced in decays of the top quark, $$t \rightarrow H^{\pm } b$$ t → H ± b with $$H^{\pm } \rightarrow cs$$ H ± → c s , is presented. This search targets the production of top-quark pairs $$t\bar{t} \rightarrow Wb H^{\pm } b$$ t t ¯ → W b H ± b , with $$W \rightarrow \ell \nu $$ W → ℓ ν ( $$\ell = e, \mu $$ ℓ = e , μ ), resulting in a lepton-plus-jets final state characterised by an isolated electron or muon and at least four jets. The search exploits b-quark and c-quark identification techniques as well as multivariate methods to suppress the dominant $$t\bar{t}$$ t t ¯ background. The data analysed correspond to $$140\hbox { fb}^{-1}$$ 140 fb - 1 of $$pp$$ pp collisions at $$\sqrt{s} = 13\hbox { TeV}$$ s = 13 TeV recorded with the ATLAS detector at the LHC between 2015 and 2018. Observed (expected) 95% confidence-level upper limits on the branching fraction $$\mathscr {B}(t\rightarrow H^{\pm } b)$$ B ( t → H ± b ) , assuming $$\mathscr {B}(t\rightarrow Wb) + \mathscr {B}(t \rightarrow H^{\pm } (\rightarrow cs)b)=1.0$$ B ( t → W b ) + B ( t → H ± ( → c s ) b ) = 1.0 , are set between 0.066% (0.077%) and 3.6% (2.3%) for a charged Higgs boson with a mass between 60 and 168 GeV.