This paper describes an analysis of the angular distribution of W -> e nu and W -> mu nu decays, using data from pp collisions at root 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 f(0), f(L) and f(R) over two ranges of W transverse momentum (p(T)(W)) : 35 < p(T)(W) < 50 GeV and p(T)(W) > 50 GeV. Good agreement is found with theoretical predictions. For p(T)(W) > 50 GeV, the values of f(0) and f(L) - f(R), averaged over charge and lepton flavour, are measured to be: f(0) = 0.127 +/- 0.030 +/- 0.108 and f(L) - f(R) = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.