A search for a light charged Higgs boson produced in decays of the top quark, t→H±b with H±→cs, is presented. This search targets the production of top-quark pairs tt¯→WbH±b, with W→ℓν (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 tt¯ background. The data analysed correspond to 140fb-1 of pp collisions at s=13TeV recorded with the ATLAS detector at the LHC between 2015 and 2018. Observed (expected) 95% confidence-level upper limits on the branching fraction B(t→H±b), assuming B(t→Wb)+B(t→H±(→cs)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.