1539 - 1953
The following list is the most complete I have been able to find. There are some gaps , but for the most part, these are fairly short periods.
1539 - 1546 = Roger Carne
1554 - 1578 = Rees Meirick
c.1590 = Thomas Williams
c.1612 = Edmund Thomas
1621 - 1640 = William Thomas
1650 = William Morgan
1676 - 1699 = William Thomas
1708 - 1727 = Edward Jenkins
1727 - 1729 = Michael Richards of Cardiff
1730 - 1763 = John Phillips
1763 - 1794 = Thomas Edwards of Cardiff
1795 - 1797 = Henry Hollier
1798 - 1815 = John Wood (the elder)
1815 - 1846 = John Wood (the younger)
1846 - 1878 = Thomas Dalton
1878 - 1928 = Sir Thomas Mansel Franklen
1929 - 1943 = Henry David Rowland
1943 - 1953 = David James Parry