Double-differential dijet cross-sections measured in pp collisions at the LHC with a 7 TeV centre-of-mass energy are presented as functions of dijet mass and half the rapidity separation of the two highest-p(T) jets. These measurements are obtained using data corresponding to an integrated luminosity of 4.5 fb(-1), recorded by the ATLAS detector in 2011. The data are corrected for detector effects so that cross-sections are presented at the particle level. Cross-sections are measured up to 5 TeV dijet mass using jets reconstructed with the anti-k(t) algorithm for values of the jet radius parameter of 0.4 and 0.6. The cross-sections are compared with next-to-leading-order perturbative QCD calculations by NLOJet++ corrected to account for non-perturbative effects. Comparisons with POWHEG predictions, using a next-to-leading-order matrix element calculation interfaced to a parton-shower Monte Carlo simulation, are also shown. Electroweak effects are accounted for in both cases. The quantitative comparison of data and theoretical predictions obtained using various parameterizations of the parton distribution functions is performed using a frequentist method. In general, good agreement with data is observed for the NLOJet++ theoretical predictions when using the CT10, NNPDF2.1 and MSTW 2008 PDF sets. Disagreement is observed when using the ABM11 and HERAPDF1.5 PDF sets for some ranges of dijet mass and half the rapidity separation. An example setting a lower limit on the compositeness scale for a model of contact interactions is presented, showing that the unfolded results can be used to constrain contributions to dijet production beyond that predicted by the Standard Model.