History of Lindisfarne Priory
Lindisfarne – also known as Holy Island – was the site of the earliest Christian monastery in Anglo-Saxon Northumbria and one of the most important centres of early Christianity in England. Irish monks settled here in AD 635 at the invitation of the Northumbrian king, and the monastery became the centre of a major saint’s cult celebrating its bishop, Cuthbert. It was here that the masterpiece now known as the Lindisfarne Gospels was created in the early 8th century. The ruins now visible are those of a small priory established in the 12th century by monks from Durham, which claimed direct descent from the early monastery.
http://www.english-heritage.org.uk/visit/places/lindisfarne-priory/history/

The parish church stands on the site of the wooden church built by St. Aidan in 635 AD, which during the Anglo-Saxon period was replaced by a small stone church. The Benedictine monks of Durham, who in the 12th century began to build the second monastery, decided this should be the parish church and employed and paid a chaplain to care for the villagers.

The building was enlarged twice: once in the 12th century by a Romanesque north arcade and a Norman apse (now gone) and an early English south arcade and chancel in the 13th century. Parts of the original Saxon church survive in the wall containing the chancel arch. The tower and the porch were added later.

More information can be found here
http://www.stmarysholyisland.org.uk/tour.htm
It is in this church that the copy of the original Gospels of Lindisfarne can be viewed.