Im no expert but this map shows the Bury is not part of the Priory boundaries

Look closely at this map available in a document on Tendring District Councils website which clearly shows the boundary of the Priory, and the Bury is not included.

St Osyth Boundary Map

The full Document is available from Tendring District Councils Website which incidentally makes reference to the Bury as The Green. But when you view the Tendring District Conservation review document the council refers to the Bury as the Village Green! Look for yourself at the Conservation Document here

Also have a look at the historic map in this conservation document, this also shows the Bury is not part of the Priory! and this document was created March 2006.