A search has been performed for pair production of heavy vectorlike down-type (B) quarks. The analysis explores the lepton-plus-jets final state, characterized by events with one isolated charged lepton (electron or muon), significant missing transverse momentum, and multiple jets. One or more jets are required to be tagged as arising from b quarks, and at least one pair of jets must be tagged as arising from the hadronic decay of an electroweak boson. The analysis uses the full data sample of pp collisions recorded in 2012 by the ATLAS detector at the LHC, operating at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb-1. No significant excess of events is observed above the expected background. Limits are set on vectorlike B production, as a function of the B branching ratios, assuming the allowable decay modes are B→Wt/Zb/Hb. In the chiral limit with a branching ratio of 100% for the decay B→Wt, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 810 GeV (760 GeV). In the case where the vectorlike B quark has branching ratio values corresponding to those of an SU(2) singlet state, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 640 GeV (505 GeV). The same analysis, when used to investigate pair production of a colored, charge 5/3 exotic fermion T5/3, with subsequent decay T5/3→Wt, sets an observed (expected) 95% C.L. lower limit on the T5/3 mass of 840 GeV (780 GeV).