Searches for electroweak production of wino-like chargino pairs, χ~1+χ~1−, and of wino-like chargino and next-to-lightest neutralino, χ~1±χ~20, are presented. The models explored assume that the charginos decay into a W boson and the lightest neutralino, χ~1±→W±χ~10. The next-to-lightest neutralinos are degenerate in mass with the chargino and decay to χ~10 and either a Z or a Higgs boson, χ~20→Zχ~10 or hχ~10. The searches exploit the presence of a single isolated lepton and missing transverse momentum from the W boson decay products and the lightest neutralinos, and the presence of jets from hadronically decaying Z or W bosons or from the Higgs boson decaying into a pair of b-quarks. The searches use 139 fb−1 of s = 13 TeV proton-proton collisions data collected by the ATLAS detector at the Large Hadron Collider between 2015 and 2018. No deviations from the Standard Model expectations are found, and 95% confidence level exclusion limits are set. Chargino masses ranging from 260 to 520 GeV are excluded for a massless χ~10 in chargino pair production models. Degenerate chargino and next-to-lightest neutralino masses ranging from 260 to 420 GeV are excluded for a massless χ~10 for χ~20→Zχ~10. For decays through an on-shell Higgs boson and for mass-splitting between χ~1±/χ~20 and χ~10 as small as the Higgs boson mass, mass limits are improved by up to 40 GeV in the range of 200–260 GeV and 280–470 GeV compared to previous ATLAS constraints.