Gauge boson production at forward rapidities in single diffractive events at the LHC is investigated considering pp collisions at $$\sqrt{s} =$$ s = 8 and 13 TeV. The impact of gap survival effects is analysed using two different models for the soft rescattering contributions. We demonstrate that using the forward shower counter Project at LHCb–HERSCHEL, together with the Vertex Locator–VELO, it is possible to discriminate diffractive production of the gauge bosons $${W}$$ W and $${Z}$$ Z from the non-diffractive processes and studies of the Pomeron structure and diffraction phenomenology are feasible. Moreover, we show that the analysis of this process can be useful to constrain the modelling of the gap survival effects.