There were several Morgan families in Carmarthenshire from which this MP may have come, but his name does not occur at the appropriate time in any of their pedigrees. The 1563 election return shows that he was a burgess of Carmarthen.
One, and one only, source for names of Members of the 1571 Parliament has a John Morgan sitting for Carmarthen Boroughs. This is the list Browne Willis printed from a manuscript formerly in the collection of Le Neve;
The indications are that the John Morgan who sat for Carmarthen in 1563 was not the sewer of the Queen’s chamber who began to acquire land in Carmarthenshire and Cardiganshire from 1586.
