The increase in luminosity and center of mass energy at the FCC-hh will open up new clean channels where BSM contributions are enhanced at high energy. In this paper we study one such channel, $Wh to ell ugammagamma$. We estimate the sensitivity to the $mathcal{O}_{varphi q}^{(3)}$, $mathcal{O}_{varphi {W}}$, and $mathcal{O}_{varphi widetilde {W}}$ SMEFT operators. We find that this channel will be competitive with fully leptonic $WZ$ production in setting bounds on $mathcal{O}_{varphi q}^{(3)}$. We also find that the double differential distribution in the $p_T^h$ and the leptonic azimuthal angle can be exploited to enhance the sensitivity to $mathcal{O}_{varphi widetilde {W}}$. However, the bounds on $mathcal{O}_{varphi {W}}$ and $mathcal{O}_{varphi widetilde {W}}$ we obtain in our analysis, though complementary and more direct, are not competitive with those coming from other measurements such as EDMs and inclusive Higgs measurements.
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