A search for a massive resonance ${\mathrm{W}^{\prime }}$ decaying into a W and a Higgs boson in the $\ell \nu \mathrm{b} \overline{\mathrm{b}} $ ( $\ell = \mathrm {e}$ , $\mu $ ) final state is presented. Results are based on data corresponding to an integrated luminosity of 19.7 $,\text {fb}^{{-1}}$ of proton–proton collisions at $\sqrt{s}=8$ $~\text {TeV}$ , collected using the CMS detector at the LHC. For a high-mass ( $\gtrsim $ 1 $~\text {TeV}$ ) resonance, the two bottom quarks coming from the Higgs boson decay are reconstructed as a single jet, which can be tagged by placing requirements on its substructure and flavour. Exclusion limits at 95 % confidence level are set on the production cross section of a narrow resonance decaying into WH, as a function of its mass. In the context of a little Higgs model, a lower limit on the ${\mathrm{W}^{\prime }}$ mass of 1.4 $~\text {TeV}$ is set. In a heavy vector triplet model that mimics the properties of composite Higgs models, a lower limit on the ${\mathrm{W}^{\prime }}$ mass of 1.5 $~\text {TeV}$ is set. In the context of this model, the results are combined with related searches to obtain a lower limit on the ${\mathrm{W}^{\prime }}$ mass of 1.8 $~\text {TeV}$ , the most restrictive to date for decays to a pair of standard model bosons.