The Fermi Large Area Telescope discovered the time signature of a radio-silent pulsar coincident with RX J0007.0+7302, a plerion-like X-ray source at the centre of the CTA 1 supernova remnant. The inferred timing parameters of the ...-ray pulsar PSR J0007+7303 (...) point to a Vela-like neutron star, with an age comparable to that of CTA 1. The PSR J0007+7303 low distance (~1.4 kpc), interstellar absorption (AV ~ 1.6), and relatively high energy loss rate (...), make it a suitable candidate for an optical follow-up. Here, we present deep optical observations of PSR J0007+7303. The pulsar is not detected in the Gran Telescopio Canarias images down to a limit of ..., the deepest ever obtained for this pulsar, while William Herschel Telescope images yield a limit of V ~ 26.9. Our ...-band limit corresponds to an optical emission efficiency ... This limit is more constraining than those derived for other Vela-like pulsars, but is still above the measured optical efficiency of the Vela pulsar. We compared the optical upper limits with the extrapolation of the XMM-Newton X-ray spectrum and found that the optical emission is compatible with the extrapolation of the X-ray power-law component, at variance with what is observed, e.g. in the Vela pulsar. (ProQuest: ... denotes formulae/symbols omitted.)