However, mediaeval historians generally accept that “Lothian” (south-east Scotland) was granted to Kenneth of Scotland by Edgar of England around 975.
My academic research on this very subject shows that Malcolm, as was traditional for new Scottish kings then, raided England in 1006 and was defeated at Durham by Uhtred.
Later, Uhtred deserted King Æthelred for Cnut, his rival who gave him responsibility for guarding the north. Badly undermanned, he was too tempting a target for Malcolm, doubtless still smarting from his defeat at Durham.
Uhtred was made Earl of Northumbria for the victory by Æthelred who had also devastated Strathclyde in 1000. Malcolm and Owain had scores to settle.
There is no record of “Lothian” being retaken after Durham. It remained under Scottish control and Carham was a powerful statement of ownership.
Uhtred’s men were exclusively drawn from between the Tees and the Tweed.
In 1016, both claimants to the English throne were fighting in the south and Malcolm could attack Uhtred with impunity. By 1018, Cnut was King of England and it was too late for Malcolm to attack. Cnut had Uhtred murdered. Carham was a good excuse. Yet, when Cnut invaded Scotland about 1031, he did not seize back Lothian, because he knew that it had been, both de jure and de facto, part of the Scottish realm from around 975.
Carham confirmed existing Scottish ownership of “Lothian”. It did not win that territory.
Andrew HN Gray MSc (Medieval History)