The decision of the question seems to depend upon whether we should regard the Goidelic elements visible in western Britain as due in part to an original Goidelic population or ascribe them wholly to Irish immigrants.
"The Romanization of Roman Britain"
F. Haverfield
Picts, Goidelic Celts, Brythonic Celts, Scots, and Anglo-Saxons were in possession of the country.
"An Outline of the Relations between England and Scotland (500-1707)"
Robert S. Rait