I have a different perspective. The three plumes (heraldically, they’re ostrich feathers) have no particular historical association to Wales as a country and don’t indicate that the button was made in Wales. The plumes (often with the German motto “Ich Dien” meaning “I Serve”) were first adopted by British royalty by the ‘Black Prince’ (eldest son of Edward III of England and heir to the throne) after his victory at the Battle of Crécy in 1346. Thereafter they have particular association in Britain to the Prince of Wales as opposed to the country of Wales. It’s an honorary title that has usually been bestowed on the next-in-line to the British throne since 1301 and merges with the Crown on accession. The current Prince of Wales is Prince Charles, who uses the plumes, but he’s no more Welsh than I am.
Without better visibility of the backmark it’s difficult to say, but the button may have been made by one of the Jennens companies of London, England. Jennens & Co used the PoW plumes as a backmark from 1860 until about 1910 (perhaps 1912 at the latest), probably because they had Royal patronage from Prince Edward at the time (later Edward VII), but lost it when he died in 1910 and the PoW title passed to the Edward who became Edward VIII but then abdicated. Their forerunners such as Charles Jennens also used the plumes during the period c1800-1832.
It may be my imagination and perhaps you can see better in hand, but I fancy I can see the letters “…NDO…” at the top (as part of “LONDON”?).
[Note also that Ireland is not part of the United Kingdom. At least not now. It’s a completely separate country (also known as the Republic of Ireland) with its own government, passports, currency (euro) and membership of the EU. When Ireland partitioned in 1921, only the six counties in the northeast chose to remain in the United Kingdom, collectively becoming “Northern Ireland” to make the distinction. Sorry if that seems a bit pedantic, but try telling someone from Ireland that they're "British" and see what reaction you get!]
