I did a bit of research into the history of Wales on this site. There was continuous English involvement in Wales from the time of the Norman Conquest. Then:
In 1294, the Statute of Rhuddlan confirmed Edward's plans regarding the governing of Wales (apart from the Marches, left more or less as quasi-independent earldoms as rewards for their help in disposing of the Welsh problem). The statute created the counties of Anglesey, Caernarfon and Merioneth, to be governed by the Justice of North Wales; Flint, to be placed under the Justice of Chester and the counties of Carmarthen and Cardigan to be left under the Justice of South Wales.Moving on to the sixteenth century:In the new counties the English pattern of courts was firmly set in place though some Welsh Law was retained in a few civil actions, mainly concerning minor land disputes. The Welsh counties did not elect representatives to Parliament; they remained outside the jurisdiction of the central courts of Westminster. Edward was more than jubilant; for all practical purposes, his troubles with the Welsh were at an end. From that time forward, Wales was to live under an alien political system, playing a subordinate role as an integral part of the kingdom of England. It was as if a nation or a people never existed.
After Henry VIII had broken with Rome, he felt ready to further show his power as rightful king of Wales as well as England. The first of the Acts of Union (a modern term describing several acts of legislation having to do with Wales) took place in 1536. Its provisions ensured the political annexation of Wales to England, for it gave notice that part of their intent was "[henceforth] . . .to utterly extirpate all and singular the sinister usage and customs differing from the same {English laws]."So, Wales was formally integrated into England in 1536 but had been subject to strong English control since 1294 and less so before then.Yet, it must be noted that the Act, one of the most important in the whole history of Wales, was passed without consultation with the Welsh people; there was no agreement of a central Welsh authority or parliament, simply because such an authority did not exist.
The difference for Scotland was that the union with England in 1707 was the result of Acts being voluntarily passed in both the Edinburgh and London parliaments to combine into a new British parliament. After 1536, then, the London parliament ruled both England and Wales but without the agreement of any Welsh legislature. You could say that it was the parliament of England and Wales or of England and its Welsh colony.