The first measurement of the charged component of the underlying event using the novel "jet-area/median" approach is presented for proton-proton collisions at centre-of-mass energies of 0.9 and 7TeV. The data were recorded in 2010 with the CMS experiment at the LHC. A new observable, sensitive to soft particle production, is introduced and investigated inclusively and as a function of the event scale defined by the transverse momentum of the leading jet. Various phenomenological models are compared to data, with and without corrections for detector effects. None of the examined models describe the data satisfactorily.