St Andrew's Church in Greensted, Essex is the oldest stave church in England. The nave is built of timbers cut in the late 11th century, but there is an earlier structure of some kind in there. St Edmund was brought here on the way to being buried in Bury St Edmund. Source.
The church of San Sylvestro in Capite in Rome stands on the site of the Roman temple of Sol Invictus, which was dedicated by the emperor Aurelian on December 25th, 274 to commemorate his victory over Palmyra in the East. The church was built on top of it in the 8th century, and refurbished in 1198, 1601 and 1681. This medieval-looking chunk of masonry, photographed by Gertrude Bell in 1910, has a hare and a green man, and looks like it came from the 1198 rebuild. Source.