This letter reports on a search for hypothetical heavy neutrinos, N, and right-handed gauge bosons, WR, in events with two high transverse momentum leptons and at least one high transverse momentum hadronic jet. The results were obtained from data corresponding to an integrated luminosity of 2.1 fb^-1 collected in proton-proton collisions at sqrt(s) = 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. No excess above the Standard Model background expectation is observed. Excluded mass regions for Majorana and Dirac neutrinos are presented using two approaches for interactions that violate lepton and lepton-flavour numbers. One approach uses an effective operator framework, the other approach is guided by the Left-Right Symmetric Model. The results described in this letter represent the most stringent limits to date on the masses of heavy neutrinos and WR bosons obtained in direct searches.