  We study the prospects of testing the $WW\gamma$ vertex in $e^- p\to\nu\gamma
X$ and $e^+ p\to\nu\gamma X$ at HERA and LEP/LHC. Destructive interference
effects between the Standard Model and the anomalous contributions to the
amplitude severely limit the sensitivity of both processes to non-standard
$WW\gamma$ couplings. Sensitivity limits for the anomalous $WW\gamma$ couplings
$\kappa$ and $\lambda$ at HERA and LEP/LHC are derived, taking into account
experimental cuts and uncertainties, and the form factor behaviour of
nonstandard couplings. These limits are found to be significantly weaker than
those which can be expected from other collider processes within the next few
years. At HERA, they are comparable to bounds obtained from $S$-matrix
unitarity.
