Distributions sensitive to the underlying event in QCD jet events have been measured with the ATLAS detector at the LHC, based on (Formula presented.) of proton–proton collision data collected at a centre-of-mass energy of 7 (Formula presented.). Charged-particle mean (Formula presented.) and densities of all-particle (Formula presented.) and charged-particle multiplicity and (Formula presented.) have been measured in regions azimuthally transverse to the hardest jet in each event. These are presented both as one-dimensional distributions and with their mean values as functions of the leading-jet transverse momentum from 20 to 800 (Formula presented.). The correlation of charged-particle mean (Formula presented.) with charged-particle multiplicity is also studied, and the (Formula presented.) densities include the forward rapidity region; these features provide extra data constraints for Monte Carlo modelling of colour reconnection and beam-remnant effects respectively. For the first time, underlying event observables have been computed separately for inclusive jet and exclusive dijet event selections, allowing more detailed study of the interplay of multiple partonic scattering and QCD radiation contributions to the underlying event. Comparisons to the predictions of different Monte Carlo models show a need for further model tuning, but the standard approach is found to generally reproduce the features of the underlying event in both types of event selection.