This article presents a search for a heavy charged Higgs boson produced in association with a top quark and a bottom quark, and decaying into a W boson and a 125 GeV Higgs boson h. The search is performed in final states with one charged lepton, missing transverse momentum, and jets using proton-proton collision data at s = 13 TeV recorded with the ATLAS detector during Run 2 of the LHC at CERN. This data set corresponds to a total integrated luminosity of 140 fb−1. The search is conducted by examining the reconstructed invariant mass distribution of the Wh candidates for evidence of a localised excess in the charged Higgs boson mass range from 250 GeV to 3 TeV. No significant excess of data over the expected background is observed and 95% confidence-level upper limits between 2.8 pb and 1.2 fb are placed on the production cross-section times branching ratio for charged Higgs bosons decaying into Wh.