A bstract A search for Higgs boson pair production in the $$ b\overline{b}W{W}^{*} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>W</mml:mi> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>*</mml:mo> </mml:msup> </mml:math> decay mode is performed in the $$ b\overline{b}\mathit{\ell \nu qq} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ℓνqq</mml:mi> </mml:math> final state using 36.1 fb −1 of proton-proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. No evidence of events beyond the background expectation is found. Upper limits on the non-resonant pp → HH production cross section of 10 pb and on the resonant production cross section as a function of the HH invariant mass are obtained. Resonant production limits are set for scalar and spin-2 graviton hypotheses in the mass range 500 to 3000 GeV.