Abstract: A search for flavour-changing neutral current decays of a top quark to an up-type quark (q = u; c) and the Standard Model Higgs boson, where the Higgs boson decays to b (b) over bar, is presented. The analysis searches for top quark pair events in which one top quark decays to W b, with the W boson decaying leptonically, and the other top quark decays to Hq. The search is based on pp collisions at root s = 8TeV 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 t (t) over bar -> 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 -> gamma gamma and H -> WW*, tau tau 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 vertical bar lambda(tcH)vertical bar and vertical bar lambda(tuH)vertical bar couplings are 0.13 (0.10) and 0.13 (0.10) respectively. These are the most restrictive direct bounds on t q H interactions measured so far.