This button was shared by a reader:
Woolwich is a market town and parish on the River Thames, 8 miles SE of London. In 1833 the dissolution of the partnership of Joesph & Edward Grisbrook was noted in the London Gazette. Edward died in 1851, with the firm becoming Joseph Grisbrook & Co.
J. Grisbrook & Co operated from 46-48 Powis Street, Woolwich, as linen and woollen drapers, upholsterers and furnishing warehousemen from around 1840 until 1862, when the business was bought out by partner F. A. Wallis , Joseph having come to a sad and grisly end in 1861. The business was then known as Wallis & Howes.
The design for Royal Artillery uniform buttons (both for regular and volunteer troops) showing 3 cannons pointing left under the Royal crown date from 1831-1840, then from 1855-1873.
Therefore button shared above dates from 1855-1861, and would have been produced for use in Britain. If it was worn by NSW or Victorian artillery (and it is possible that old buttons were reused), it would date from 1870-1873, as volunteer troops were not formed until after the withdrawal of British forces in 1870; then in 1873, the button design changed to that of an artillery field gun pointing left, under the Royal Crown.