New neutral vector bosons Z′ decaying to charged gauge boson pairs W+W− are predicted in many scenarios of new physics, including models with an extended gauge sector such as E6, left-right symmetric ZLRS′ and the sequential standard model ZSSM′. For these benchmark models we calculate and present theoretical expectations for different values of the Z′ mass M2 and mixing parameter ξ. Our results are based on the narrow width approximation which allows for the making of a convenient comparison of the experiment to theoretical benchmark models. The diboson production allows for the placement of stringent constraints on the Z−Z′ mixing angle and the Z′ mass, which we determine by using data from pp collisions at s=13 TeV recorded by the ATLAS detector at the CERN LHC, with integrated luminosity of ∼36 fb−1. By comparing the experimental limits to the theoretical predictions for the total cross section of Z′ resonant production and its subsequent decay into W+W− pairs, we show that the derived constraints on the mixing angle for the benchmark models are of the order of a few ×10−4, i.e., greatly improved with respect to those derived from the global analysis of electroweak data. We combine the limits derived from diboson production data with those obtained from the Drell–Yan process in order to significantly extend the exclusion region in the M2−ξ parameter plane. Also, we demonstrate that further improvement on the constraining of this mixing can be achieved through analysis of the full set of Run II data.