This paper presents searches for the direct pair production of charged light-flavour sleptons, each decaying into a stable neutralino and an associated Standard Model lepton. The analyses focus on the challenging “corridor” region, where the mass difference, ∆m, between the slepton ($ \overset{\sim }{e} $ or $ \overset{\sim }{\mu } $) and the lightest neutralino ($ {\overset{\sim }{\chi}}_1^0 $) is less or similar to the mass of the W boson, m(W), with the aim to close a persistent gap in sensitivity to models with ∆m ≲ m(W). Events are required to contain a high-energy jet, significant missing transverse momentum, and two same-flavour opposite-sign leptons (e or μ). The analysis uses pp collision data at $ \sqrt{s} $ = 13 TeV recorded by the ATLAS detector, corresponding to an integrated luminosity of 140 fb$^{−1}$. Several kinematic selections are applied, including a set of boosted decision trees. These are each optimised for different ∆m to provide expected sensitivity for the first time across the full ∆m corridor. The results are generally consistent with the Standard Model, with the most significant deviations observed with a local significance of 2.0 σ in the selectron search, and 2.4 σ in the smuon search. While these deviations weaken the observed exclusion reach in some parts of the signal parameter space, the previously present sensitivity gap to this corridor is largely reduced. Constraints at the 95% confidence level are set on simplified models of selectron and smuon pair production, where selectrons (smuons) with masses up to 300 (350) GeV can be excluded for ∆m between 2 GeV and 100 GeV.[graphic not available: see fulltext]