jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe present the two-loop leading colour QCD helicity amplitudes for the process jats:italicpp → W</jats:italic> (jats:italic→ lν</jats:italic>)jats:italicγ</jats:italic> + jats:italicj</jats:italic>. We implement a complete reduction of the amplitudes, including the leptonic decay of the jats:italicW</jats:italic>-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders for physical kinematics, and hence the suitability for phenomenological applications.</jats:p>