The primary source which confirms her parentage and marriage has not yet been identified. 1
Marriage Information:
Ælfgifu married Ælfgar III, Earl of East Anglia & Mercia, son of Leofric III of Mercia, Lord of Coventry, and Lady Godgyfu of Lincoln, Countess of Mercia. (Ælfgar III, Earl of East Anglia & Mercia, died about 1062 and was buried in Coventry, Warwickshire, England.)
Sources
1 Foundation for Medieval Genealogy, Medlands, Ælfgifu.