When did Wales join the UK?

The principality was brought under English control in 1284 when the Statute of Rhuddlan was enacted, the remaining Welsh territory was administered under the Marcher Lords until the Laws in Wales acts of 1536 (and 1542) were passed making England and Wales a single legal state. Sometimes referred to as the Act of Union between England and Wales similar to the Scottish/English Act although the naming of it as such is unofficial and didn't occur until the 20th century.

The Crowns of England and Scotland were joined in 1603 and the Parliaments joined under the Act of Union in 1707 being known as the Kingdom of Great Britain. However it was not until the union of 1801 that the title the United Kingdom of Great Britain and Ireland came in to being and therefore technically the answer as to Wales joining the UK is 1801.

If you mean england 1284 but otherwise 1801.