Searches in final states with two leptons plus missing transverse energy, targeting supersymmetric particles or invisible decays of the Higgs boson, were performed during Run 1 of the LHC. Recasting the results of these analyses in the context of the inert doublet model (IDM) using MadAnalysis 5, we show that they provide constraints on inert scalars that significantly extend previous limits from LEP. Moreover, these LHC constraints allow us to test the IDM in the limit of very small Higgs–inert scalar coupling, where the constraints from direct detection of dark matter and the invisible Higgs width vanish.