A measurement of splitting scales, as defined by the kT clustering algorithm, is presented for final states containing a W boson produced in proton-proton collisions at a centre-of-mass energy of 7 TeV. The measurement is based on the full 2010 data sample corresponding to an integrated luminosity of 36 pb(-1) which was collected using the ATLAS detector at the CERN Large Hadron Collider. Cluster splitting scales are measured in events containing W bosons decaying to electrons or muons. The measurement comprises the four hardest splitting scales in a k(T) cluster sequence of the hadronic activity accompanying the W boson, and ratios of these splitting scales. Backgrounds such as multi-jet and top-quark-pair production are subtracted and the results are corrected for detector effects. Predictions from various Monte Carlo event generators at particle level are compared to the data. Overall, reasonable agreement is found with all generators, but larger deviations between the predictions and the data are evident in the soft regions of the splitting scales.