A study of W+W− events accompanied by hard photon radiation, Eγ>2.5 GeV, produced in e+e− collisions at LEP is presented. Events consistent with being two on-shell W-bosons and an isolated photon are selected from 681 pb−1 of data recorded at 180 GeV<s<209 GeV. From the sample of 187 selected W+W−γ candidates with photon energies greater than 2.5 GeV, the W+W−γ cross-section is determined at five values of s. The results are consistent with the Standard Model expectation. Averaging over all energies, the ratio of the observed cross-section to the Standard Model expectation is R(data/SM)=0.99±0.09±0.04, where the errors represent the statistical and systematic uncertainties respectively. These data provide constraints on the related O(α) systematic uncertainties on the measurement of the W-boson mass at LEP. Finally, the data are used to derive 95% confidence level upper limits on possible anomalous contributions to the W+W−γγ and W+W−Z0γ vertices: −0.020 GeV−2<a0Λ2<0.020 GeV−2,−0.053 GeV−2<acΛ2<0.037 GeV−2,−0.16 GeV−2<anΛ2<0.15 GeV−2, where Λ represents the energy scale for new physics and a0, ac and an are dimensionless coupling constants.