You've got: modern encyclopedia entries and a couple of website links you probably found off of google.
I've got:
1. The Romans, who named the island Britanniae, the home of the Britons.
2. Geoffrey of Monmouth, who universalized the use of the term Britanniae, or Britannia, as the geographical name of the island that has stood until the modern era.
3. The Journal of the House of Commons from 1604 when the political distinction was formalized.
So what then is the stronger evidence? Original historical source material or your encyclopedia entries? As I noted previously, most people learn around high school or college that encyclopedias may work for book reports in the sixth grade, but they do not meet the standards of academic research.
Gratias tibi doctor care, qui hec michi dignatus es aperire et tantum boni conferre tam michi quam omnibus illis quibus istum librum contingat perlegere.
I'll catch you on the next epicycle.