Andy Furey is the National Officer for Communication Workers Union, which represents staff working in Crown Post Offices.
He told ITV News: "A Welsh town like Holywell needs a Crown Post Office. If we lose it, this could be the death knell for the high street in Holywell."
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Fire crews have been responding to reports of flash flooding in Carmarthenshire. Some homes have been affected.
Medication designed for animals was taken from the building in Abertillery on Thursday night.
More than a thousand riders will be taking part in a series of events in and around the town.