There wasn't always Sunday drinking in Wales.
Wiki:
[ The Sunday Closing (Wales) Act 1881 was an Act of the Parliament of the United Kingdom. It was one of the Licensing Acts 1828 to 1886.[1] It required the closure of all public houses in Wales on Sundays. The Act had considerable political importance as a formal acknowledgement of the separate character of Wales, setting a precedent for future legislation and decisions. It was repealed in 1961.]

I think it was around 2003 before all pubs in Wales opened for alcohol consumption. I believe in Ireland, the pubs close for one hour a day to wash the glasses ;)

I've never heard of 'welshing', but welching (on a bet) is common enough.