Said with a little local insight, for many in North Wales, that would be considered to be Liverpool.North Wales is not part of North-West England and requires connectivity to its capital city.
Anyway! Due to the geography and numbers of people involved, the obvious solution is as JCollins suggests, to look beyond "national" boundaries and consider the practical. In addition to the Holyhead to Liverpool via Runcorn services (which wouldn't be Merseyrail third rail, by the by), the solution to connecting North Wales with South Wales is to connect major city to major city and have east-west intersect with that.
A Liverpool via Runcorn to Cardiff service, with which North Walians can connect to via decent services to Runcorn as well as Crewe could get them to Cardiff faster, more frequently and in more comfort than via an bi-hourly DMU trundling through Chirk which only then limits the number of useful commuter services from places like Wrexham.
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