A search for resonant diboson production using a data sample corresponding to $4.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected by the ATLAS experiment at the Large Hadron Collider in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ is presented. The search for a narrow resonance in the $WW$ or $WZ$ mass distribution is conducted in a final state with an electron or a muon, missing transverse momentum, and at least two jets. No significant excess is observed and limits are set using three benchmark models: $WW$ resonance masses below 940 and 710 GeV are excluded at 95% confidence level for spin-2 Randall--Sundrum and bulk Randall--Sundrum gravitons, respectively; $WZ$ resonance masses below 950 GeV are excluded at 95% confidence level for a spin-1 extended gauge model ${W}^{\ensuremath{'}}$ boson.