A search for flavour-changing neutral current decays of a top quark to an uptype quark (q = u, c) and the Standard Model Higgs boson, where the Higgs boson decays to bb¯¯, is presented. The analysis searches for top quark pair events in which one top quark decays to Wb, with the W boson decaying leptonically, and the other top quark decays to Hq. The search is based on pp collisions at s√=8 TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and uses 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 and at least four jets. The search exploits the high multiplicity of b-quark jets characteristic of signal events, and employs a likelihood discriminant that uses the kinematic differences between the signal and the background, which is dominated by tt¯→WbWb decays. No significant excess of events above the background expectation is found, and observed (expected) 95% CL upper limits of 0.56% (0.42%) and 0.61% (0.64%) are derived for the t → Hc and t → Hu branching ratios respectively. The combination of this search with other ATLAS searches in the H → γγ and H → WW*, ττ decay modes significantly improves the sensitivity, yielding observed (expected) 95% CL upper limits on the t → Hc and t → Hu branching ratios of 0.46% (0.25%) and 0.45% (0.29%) respectively. The corresponding combined observed (expected) upper limits on the |λtcH| and |λtuH| couplings are 0.13 (0.10) and 0.13 (0.10) respectively. These are the most restrictive direct bounds on tqH interactions measured so far.