Dear Gaëtan,
Two parrot bones were found in post-medieval contexts from Norwich. They are reported in the following publications (you can download them both in my
academia.edu page):
Albarella U. , Beech M., Locker A., Moreno-García M., Mulville J. & Curl J . 2009 . Norwich Castle : Excavations and Historical Surveys 1987-98. Part III: a Zooarchaeological Study. Norwich : East Anglian Archaeology Occasional Paper.
Albarella U. & Thomas R. 2002 They dined on crane: bird consumption, wild fowling and status in medieval England. In: Proceedings of the 4th Meeting of the ICAZ Bird Working Group Kraków, Poland, 11-15 September, 2001. Acta Zoologica Cracoviensa 45 (special issue), 23-38.
If you have found some that would be interesting to hear. At the time I could not find any parallels.
Best wishes,
Umberto