EDIT: AMADÁN AIBREÁIN! This isn't actually true. My 'quote' is actually some poorly-translated Pogues lyrics, although the Irish language doesn't actually have a verb indicating possession.

Interesting question! The process of colonization began in the 12th century with the Cambro-Norman invasion of Leinster and the subsequent establishment of Hiberno-Norman dynasties and a region around Dublin controlled directly by the English crown known as “the Pale”. The Hiberno-Normans acted mostly autonomously and were assimilated into Irish society, but English settlement was encouraged within the Pale because of an error in translation. Before the 12th century, they had almost no knowledge of Irish social or economic practices, but were familiar with the urban Scandinavians who inhabited Dublin, as they were ecclesiastically subordinate to the Archbishop of Canterbury and frequently traded with English cities, especially York.

When first establishing the Pale of settlement, the English saw Scandinavian-style farm layouts in the immediate vicinity of Dublin and assumed that all agriculture in Leinster was done by the descendants of the Norse Kingdom of Dublin. This belief was compounded by their interactions with the native Irish aristocracy. When surveying the province of Leinster to determine the best defensible boundaries of the new zone of English control in 1173, a locally ruling member of the Uí Ceinnselaig dynasty was consulted about the size of his realm. The surveyors recorded his statements for to be read in the Dublin Parliament:

Tá an talamh seo linne. Bhí sé le ár sinsir ar feadh aoiseanna.

Literally translated, this statement reads “the land here is with us. It was with our ancestors for ages”.

The Irish language does not have an equivalent verb to indicate possession such as ‘to have’ or ‘to own’. Things can be described as ‘with’, ‘at’ or ‘on’ an individual, but they do not possess it. This was interpreted by the government of the Pale to mean that the Irish had no concept of the ownership of property; they were perceived as nomadic tribes who shared all their possessions. Consequently, the government believed that the Irish who did engage in agricultural production were inhabiting farms built by the Scandinavians, and had no qualms with taking the land for themselves. Henry II then ordered the establishment of English settlements within the Pale, though they too began to intermarry with the native Irish, prompting the Crown to enact the Statutes of Kilkenny in 1366, which banned Englishmen from adopting Irish dress, speech or sports.

The Pale became England’s first colony, and by the 14th century, supplied the majority of food and livestock on the western Scottish Marches. A misunderstanding in translation led the English to believe that the Irish had no conception of private property and took central Leinster’s fertile plains for their own.

There are parts of Wales that were colonised to an extent - the southwest around Tenby is sometimes called "Little England Beyond Wales" and was settled as early as Norman times.

I would encourage you to look again at any sources that imply there was no English colonisation of Wales. After his conquest of Wales in the late 13th Century, Edward I intentionally created several new castles and towns throughout Wales, in order to solidify his military position there. Part of this policy was the invitation to English peasants to come and settle the newly conquered lands, and this was often undertaken by the great Marcher Lords, who used the English to settle conquered manners and towns that were newly under their control.

James Morris' The Welsh Wars of Edward I

"Edward I, Builder of Towns," Medieval Academy of America, Caroline Shillaber