Considering the The Evenhill in Canterbury?
A VT member wrote the following comment about visiting Canterbury:
The Cathedral & The Archbishop by KittyLou
I believe the Archbishop of Canterbury spends most his time in London but I know of one day went you will find him participating in a short service December 29th marks the martyrdom of St. Thomas and he will be there to lead the procession if you attend the afternoon evensong.
(I am pretty sure you would catch the Archbishop on Christmas Eve, Christmas, and Easter too -- but I haven't been in Canterbury on those days to find out.)