McGrath: Arthur was a king in "England" fighting against its take-over by the Anglo-Saxons. So it does fit that way, too. The name does seem to be used in different ways at different times, partly why it would be interesting to delve down into its origins rather wandering amongst its later use/misuse/abuse.
And yes, here "England" does include the Scottish Lowlands, if the traditions are correct....but let's not go into that. Other than to admit favouring the Arthur myth being based on the struggle of the North Britons, with the "identification" of many of the battle sites in Cumbria and the Borders. This could link "Logres" to Ida's Northumbrians, but not necessarily. There's enough evidence (such as it is) that "Arthur" moved about the country: the name could come from anywhere east of Wales.