Southampton was given a grant of murage dated 4/3/1380.
This was in the form of:-
Wording
Remission to the burgesses of Southampton, in consideration of their great expense in its fortification and defence and the departure of many from the town on that account, of their yearly farm for the same for three years from December last, on condition that all sums arising from the farm during that term be collected and employed about the enclosure and fortification of the town by survey of Bernard Brocas and Maurice Bruyn, knights. By bill of parl.
Granted by Richard II. (Regnal year 3). Granted at Westminster. Granted by bill of parl..
Details of the petition which resulted in this grant can be seen
at this link. 
Primary Sources
Maxwell Lyte, H.C. (ed), 1895,
Calendar of Patent Rolls Richard II (1377-81) Vol. 1 p. 448
online copy
Secondary Sources
Turner, H.L., 1971, Town Defences in England and Wales (London) p. 175 (dated as 1379)
Record created by Philip Davis. This record created 26/01/2009. Last updated on 03/05/2012. First published online 5/01/2013.
