  We calculate the fiducial and differential $W^{\pm}/Z^0+jet(s)$ production
cross-sections in the presence of electroweak (EW) corrections through virtual
loop contributions to the matrix elements (MEs) of the processes and real
partonic cascade emissions. The calculations are carried out for proton-proton
collisions at $\sqrt{s} = 13$ TeV, using Herwig 7 general-purpose Monte-Carlo
event generator with leading-order or next-to-leading-order MEs that are
interfaced with different parton-shower configurations. The results are
compared with precision experimental measurements from ATLAS collaboration and
with similar predictions within the $k_t$-factorisation framework, providing a
test for the validity of the newly-implemented QCD$\oplus$QED$\oplus$EW parton
shower in Herwig 7. It is shown that the inclusion of EW radiations in the
parton shower simulations improves Herwig 7's predictions in describing the
experimental data. Additionally, the inclusion of parton shower-induced real EW
emissions can take precedence over the incorporation of virtual EW corrections
for the simulation of EW-sensitive events.
