The two hundred years following Roman withdrawl from our island could be considered the "labor and delivery" of several new cultural groups. [Having delivered over 800 babies during my medical practice years, I have experienced first hand the blood, sweat, and tears that are involved in such a process.]
The Irish had the upper hand since they did not experience Roman occupation. Their Celtic roots expanded more quickly forming first the script called Ogham (Ogam). This writing used short horizontal or diagonal lines on stone slabs recording names, and imagine this...genealogies! This script has been found on the Isle of Man, Scotland, and Wales, showing the extent of early Irish influence around what I would call the "Celtic Mediterrian". [Irish Sea] By this time, Christianity introduced Latin, and some stones in Wales shown both Ogam and Latin. The Irish language formed through a branch of the Q-Celtic giving rise to the Galic tongues.
Irish expansion is also credited with the settlement of the south and south-west coast of what was to become Scotland. One of their major influences was the continuation of the Q-Celtic language in spite of Roman occupation south of Antonine Wall.
The Anglo-Saxon nation begins its history on our island starting 446. In their chronicles they use the term "Britons" until 465, where the name "Welsh" first appears. This was the Anglo-Saxon term used to describe those who spoke Latin and a Celtic tongue. The Welsh nation was still yet to give birth.
Wonderful references are found:
"The Celtic Realms", by Myles Dillion and Nora Chadwick, Castle Books, 1988.
"The Celtic World", Edited by Miranda Green, by Redwood Books, Ltd., 1996.
"A History of Ireland" by Peter and Fiona Somerset Fry, Barnes & Noble, 1988.
"The Course of Irish History" Edited by Moody and Maritn, The Mercier Press, 1984.
"The Anglo-Saxon Chronicles", translated by Anne Savage, Crescent Books, 1995.