Beaumaris was given a grant of murage dated 1414.
This was in the form of:-
Wording 
causa nvve edficacionis nove Muri lapidee circa eandem villam
Granted by Henry V.
Primary Sources 
Secondary Sources 
Soulsby, Ian, 1983, 
The Towns of Medieval Wales (Phillimore; Chichester) p. 78-80
Colvin, H.M., Brown, R.Allen and Taylor, A.J., 1963, 
The history of the King's Works Vol. 1: the Middle Ages (London) p. 403n5
Lewis, E.A., 1912, 
Medieval Boroughs of Snowdonia p. 102 
online copy
Comments 
in 1414, work was begun on building stone walls, which necessitated the destruction of 30 burgages, and further additions were made in the years 1536-38. (Soulsby)
Thirty burgages were declared 'waste' in 1414 causa nvve edficacionis nove Muri lapidee (sic) circa eandem villam (SC 6/1152/5). (HKW)
The town was apparently  badly protected until after the rising of Glyndwr, when Gilbert,  Lord Talbot, the reorganiser of the decayed boroughs of  Anglesea after the devastations of the rebels, appropriated thirty  of the town burgages for the purpose of building a new stone  wall round the town. (fn.. Min. Acc. 1152-5 (temp. 1409-14). Cf. ib., 1216-2 ) (Lewis)
As stated this is evidence of wall being constructed but not of royal funding, but primary source is part of Ministers' and Receivers' Accounts so works probably being done under royal authority.
     
Record created by Philip Davis. This record created 25/04/2009. Last updated on 05/01/2013. First published online 5/01/2013.