Carmarthen (Kermerdyn) was given a grant of murage dated 22/6/1326.
This was in the form of:-
Wording 
Grant to the bailiffs and good men of Kermerdyn of murage for three years. By K.
Granted by Edward II. (Regnal year 19). Granted at Tower of London. Granted by K..
Details of the petition which resulted in this grant can be seen 
at this link. 
Primary Sources 
Maxwell Lyte, H.C. (ed), 1904, 
Calendar of Patent Rolls Edward II (1324-27) Vol. 5 p. 278 
online copy
Secondary Sources 
Coulson, Charles, 2009, Murage Grants (Handwritten list and notes)
     
Record created by Philip Davis. This record created 14/01/2009. Last updated on 03/05/2012. First published online 5/01/2013.