www.adderton.co.uk

"The surname Adderton (spelled variously Aderton, Atterton, Addington, Athyerton, Adderson, Addereton, etc) is English in origin, derived from the place-name Adderstone in Northumberland. According to an authority, Adderstone is a late spelling of the early Eadrid's Tun, that is, 'the town of Eadrid's people' (tun is Anglo-Saxon for town). The Old English name Eadrid apparently meant 'property council,' and someone by that name probably founded the town."

Source: Richard Walser. 'Jeremiah Adderton and Some of His Decendants'

"The surname Atterton hails from the Leicestershire region, where there is a village called Atterton. Atterton, in Saxon language, apparantly means 'a fortified dwelling by a stream'."

Source: Steve Atterton. England.