You say there are not many islands at the east coast of England, but there was a large and important one (and not an island anymore now) :
Puz's comment about the Lindisfaras should incite to a study of their history - what is the criteria of an Anglian settlement, for instance. According to the OLB there were a lot of banned Frisians in Britannja, and it says that a 'tribe' named Angelara - supporting themseles on fish - came from the area between Denmark and Belgium. The Anglo-Saxons are regarded as being descended from a Germanic tribe that migrated from mainland Europe to Britain - to be sure, though, in the 5th century AD.
The Wikipedia says that the Lindisfaras established the kingom of Lindsey (Lindesege) in North Lincolnshire in the 6th century AD.
'Lindesege' means 'Linde's Island'. It is said the word Linde is derived from Proto-Brythonic *linn, which means 'pool', like also in the name Lincoln - why then 'Linde.s.ege' and not "Linns-ey"?