As we are in Wales St Asaph(city but village size ) is only ten minutes to Rhyl station.
St Asaph is one of Wales' four old cathedral cities (Bangor, St Davids, Llandaff) and was a city by means of antiquity, as opposed to having been granted city status by charter or by a monarch. It lost that status at some point in the 20th century during local government reorganisations.
If a city of antiquity changes local authority, then unless specific provisions are made to keep the city status then the powers that be at Westminster say that it lapses.
St Davids made sure to keep its smallest city status, given that it's such a tourist attraction. I don't think that Bangor has ever encountered such problems, remaining in 'Gwynedd' all along. The city of Llandaff was swallowed up by the newer city of Cardiff. Then Swansea and Newport make up the current five.