That may be true in scotland, i just don't know but is certainly not in Wales. The Welsh kingdoms once extended much further, well into Shropshire, for instance, in the north (the capital of Powys was once Wroxeter) and their language was Welsh. There was also Welsh, or a near relation, spoken in Cumbria in the early Dark Ages .
Of course Welsh or Brythonic was once spoken further east but not right across the country.
It was noticeable how the Shropshire accent thickened into that of Radnoshire that seemed to shade into a Welsh form even if the speaker was still using English as I went west. I think I remember that the original Ernest the policeman in the children's radio programme Larry the Lamb spoke with a Radnorshire accent but that was about 60 years ago.