A search for doubly charged Higgs bosons with pairs of prompt, isolated, highly energetic leptons with the same electric charge is presented. The search uses a proton–proton collision data sample at a centre-of-mass energy of 13 TeV corresponding to 36.1 $$\text {fb}^{-1}$$ of integrated luminosity recorded in 2015 and 2016 by the ATLAS detector at the LHC. This analysis focuses on the decays $$H^{\pm \pm }\rightarrow e^{\pm }e^{\pm }$$ , $$H^{\pm \pm }\rightarrow e^{\pm }\mu ^{\pm }$$ and $$H^{\pm \pm }\rightarrow \mu ^{\pm }\mu ^{\pm }$$ , fitting the dilepton mass spectra in several exclusive signal regions. No significant evidence of a signal is observed and corresponding limits on the production cross-section and consequently a lower limit on $$m(H^{\pm \pm })$$ are derived at 95% confidence level. With $$\ell ^{\pm }\ell ^{\pm }=e^{\pm }e^{\pm }/\mu ^{\pm }\mu ^{\pm }/e^{\pm }\mu ^{\pm }$$ , the observed lower limit on the mass of a doubly charged Higgs boson only coupling to left-handed leptons varies from 770 to 870 GeV (850 GeV expected) for $$B(H^{\pm \pm }\rightarrow \ell ^{\pm }\ell ^{\pm })=100\%$$ and both the expected and observed mass limits are above 450 GeV for $$B(H^{\pm \pm }\rightarrow \ell ^{\pm }\ell ^{\pm })=10\%$$ and any combination of partial branching ratios.