A bstract Fiducial and differential cross-section measurements of W + W − production in association with at least one hadronic jet are presented. These measurements are sensitive to the properties of electroweak-boson self-interactions and provide a test of perturbative quantum chromodynamics and the electroweak theory. The analysis is performed using proton-proton collision data collected at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 13 TeV with the ATLAS experiment, corresponding to an integrated luminosity of 139 fb − 1 . Events are selected with exactly one oppositely charged electron-muon pair and at least one hadronic jet with a transverse momentum of p T &gt; 30 GeV and a pseudorapidity of | η | &lt; 4 . 5. After subtracting the background contributions and correcting for detector effects, the jet-inclusive W + W − + ≥ 1 jet fiducial cross-section and W + W − + jets differential cross-sections with respect to several kinematic variables are measured. These measurements include leptonic quantities, such as the lepton transverse momenta and the transverse mass of the W + W − system, as well as jet-related observables such as the leading jet transverse momentum and the jet multiplicity. Limits on anomalous triple-gauge-boson couplings are obtained in a phase space where interference between the Standard Model amplitude and the anomalous amplitude is enhanced.