A search for pair production of vector-like quarks, both up-type (T) and down-type (B), as well as for four-top-quark production, is presented. The search is based on pp collisions at (Formula presented.) TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and corresponding to an integrated luminosity of 20.3 fb−1. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon with high transverse momentum, large missing transverse momentum and multiple jets. Dedicated analyses are performed targeting three cases: a T quark with significant branching ratio to a W boson and a b-quark (TT¯→Wb+X), and both a T quark and a B quark with significant branching ratio to a Higgs boson and a third-generation quark (TT¯→Ht+XandBB¯→Hb+X respectively). No significant excess of events above the Standard Model expectation is observed, and 95% CL lower limits are derived on the masses of the vector-like T and B quarks under several branching ratio hypotheses assuming contributions from T → Wb, Zt, Ht and B → Wt, Zb, Hb decays. The 95% CL observed lower limits on the T quark mass range between 715 GeV and 950 GeV for all possible values of the branching ratios into the three decay modes, and are the most stringent constraints to date. Additionally, the most restrictive upper bounds on four-top-quark production are set in a number of new physics scenarios.