In this paper we investigate consequences of an assumption that the discrepancy of the predicted and observed W+W- production cross sections at the LHC is caused by the missing contribution of the double Drell-Yan process (DDYP). Using our simple model of DDYP of Ref. [1] we show that inclusion of this production mechanism leads to a satisfactory, parameter-free description of the two-lepton mass distribution for 0-jet W+W- events and the four-lepton mass distribution for ZZ events. In such a scenario the Higgs-boson contribution is no longer necessary to describe the data. An experimental programme to prove or falsify such an assumption is proposed.