I was last in Newry in 2003, and they were celebrating having recently gained city status. The 1911 Britannica  calls it a town. So while you are certainly correct that a cathedral is a historical requirement to being called a city (at least in the UK), it doesn't appear to be sufficient in itself. 
In New Zealand, a much less religious place, the definition of city is based on population. I suppose it may have been different in the 19th century.-