From the start, Anna is said to have been given in marriage to King Lot of Lodonesia (Gododdin), by whom she became the mother of Gwalchmai (Gawain) and Medrod (Mordred). The late 13th century De Ortu Waluuanii says that the two fell in love whilst Lot was held hostage at Uther's Court. They had a wild love-affair and Anna fell pregnant, giving birth to the illegitimate Gawain, but sending him away (with tokens of his lineage) in order to avoid any scandal.
Wolfram's Parzival (c.1205) calls this lady Sangive. Later, around 1225, the Vulgate Merlin names her as a daughter of Queen Ygerna by her first husband and, therefore, merely Arthur's half-sister. An English adaptation, called Arthour & Merlin, refers to her as Belisent; whilst Welsh tradition names Gwalchmai as a son of Gwyar. Following the Welsh version of the 'Birth of Arthur,' this name is sometimes taken to refer to his mother, but this is unlikely.
Lot's wife and Gawain's mother is, moreover, better known by the name, Morgause, adopted by Sir Thomas Malory in his Le Morte D'Arthur (1469) for one of King Arthur's half-sisters. This form seems to have originated around 1200 in the first continuation of Chretien de Troyes' Perceval, where she is called Morcades. This is, in fact, a place-name, probably an epithet: Orcades being the Latin name for the Orkney Isles, one of the literary homes of King Lot and his wife. Thus, the lady was probably Anna Morgause: Anna of the Orkneys.
It was Morgause who supposedly enjoyed an incestuous night of passion with her half-brother, Arthur, and thus begat their son, Mordred. She had been sent to the High-King's court at Caerleon in order to assess his intentions after her husband's rebellious defeat at the Battle of Bedegraine. Arthur had not previously met his sister and was completely ignorant of their relationship. The repulsiveness of such an act has led modern authors to merge Morgause with her 'evil' sister Morgan Le Fay in this respect.
In her widowhood, Morgause entered into an affair with Lamorak, the son of her late husband's killer. She was discovered in bed with him by her own son, Gaheris (Gwalchafed), who instantly struck her down!
References to Anna/Morgause as a wife of King Budic of Brittany (alias Emyr Llydaw) are due to confusion with her sister, Elaine.