This paper describes an analysis of the angular distribution of W→eν and W→μν decays, using data from pp collisions at √s =7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb-1. Using the decay lepton transverse momentum and the missing transverse momentum, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (pWT): 35 < pWT < 50 GeV and pWT > 50 GeV. Good agreement is found with theoretical predictions. For pWT >50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be: f0=0. 127±0. 030±0. 108 and fL-fR=0. 252±0. 017±0. 030, where the first uncertainties are statistical, and the second include all systematic effects. © 2012 CERN for the benefit of the ATLAS collaboration.