The Archbishoo of Canturbury has a bishop's palace (not as grand
as it sounds - but all bishops live in 'palaces' some of which are
just large houses). This is located in Canterbury,. However he also
has an official residence in Lambeth Palace, London, which is
situated on the opposite side of the river from the House of
Parliament at the far end of Lambeth bridge, right on the banks of
the Thames. All the other archbishops (of the other provinces such
as York, Wales, Canada, etc) live in a palace usually in the
cathedral city and near the cathedral where he holds the chair as
bishop.