Recommended Websites
If you are interested in the history of the Native Police and/or archeology, take a look at
https://archaeologyonthefrontier.com/2020/09/03/buttons/
A good site for early British uniform buttons:
https://asahelena.wixsite.com/militarybuttons
Remember that many British regiments have long histories, with changes to their uniforms and buttons over time. The backmarks can help, but some of these were used over decades, presenting a challenge. See these websites for help.
https://www.ukdfd.co.uk/pages/buttonsgtom.html
https://oldcopper.org/makers/button_makers.php
https://www.angelfire.com/wa/dianaspage/BritishButtonBackmarks.html
https://www.britishbuttonsociety.com/
21st Regiment of Foot (Royal North British Fusiliers)
This regiment served in New South Wales, Western Australia and South Australia between 1833-1839. They then left for Madras, India.

The Sydney Herald, 13th December 1832 page 2.
Published in the Mirror (Perth), 19th March 1938 page 11. Oh dear.
96th Regiment of Foot (Manchester)
This regiment served in New South Wales, Tasmania and South Australia between 1839-1848, then travelling on to India. A detachment had been sent to New Zealand in 1845-6.

The Sydney Monitor and Commercial Advertiser, 9th December 1839 page 2. However, most of the regiment arrived from 1840-41.