We study the cross-section of production of a single W − boson in association with a neutrino through the process e − p → e − γ * p → ν e W − p. Additionally, we obtain the anomalous couplings ∆κ γ and λ γ of the W + W − γ vertex at the Large Hadron Electron Collider (LHeC) and the Future Circular Collider Hadron-Electron (FCC-he). The impact of the polarized beam due to the electron is also analyzed. Our best limits for ∆κ γ and λ γ at the 95% C.L. are: ∆κ γ = ±0.0017, λ γ = ±0.0053 (unpolarized electron beam) and ∆κ γ = ±0.0013, λ γ = ±0.0046 (polarized electron beam) identifying the W − boson through the hadronic decay channel. In addition, the e − γ * → ν e W − collision is one of the clean, pure and simple process to probe the W + W − γ coupling without the complications of QCD backgrounds.