The chapels contain five magnificent medieval tombs. They date from the early 14th century- and are as fine as anything anywhere. There are no names (I guess at the time you didn't need to ask) but the grandest of them almost certainly belongs to Gervase Alard- Admiral of the Western Fleet- who died in 1310.
Alard holds his heart between praying hands. I have no idea what that is about. The canopy is supported by the heads of a king and queen- allegedly Edward I and his second wife Margaret.