Pre-dating the American Revolution, Street Firing is described in Bland's "A Treatise of Military Discipline" (p86 in the 1743 5th Edition)
Street Firing did not appear in the 1792 British Regulations, but was featured in the revised 1824 Regulations (p122). It also appeared in the 1833 and, I think, the 1859 Regulations.
Regards
Mark