Mother of pearl gaming counters were ordered, rather like the armorial porcelain of which you have a set at Browsholme, via. the East India Company trading with Canton (Canton (also known as Guangzhou) had a biannual trade fair and is located in the Guangdong province in southern China.)
They were either ordered by an individual, or as a wedding present etc. They flourished from about 1720 to 1840. A full set is about 140 counters. It comes in three shapes, which denote value for playing 'Whist' and some other games that are now defunct. There were oblong counters (c80), square counters (40) and circular counters (20) - although this could vary.
You could buy an off the peg set in Canton perhaps with designs of fish or birds etc. But the serious sets are armorials (those relating to heraldry, or bearing a coat of arms). A design would be sent on one ship and perhaps picked up a year later by another. We still don't know how the Chinese craftsmen managed to do such amazing work by hand and repeated to match.
The most famous set belonged to Queen Charlotte. She lost so much money at cards that George III confiscated the set! George IV then sold it with lots of his mother's effects in order to provide a dowry for his unmarried sisters. He retained 6 counters at Windsor, an din the early 20th Century Queen Mary bought back another 7.
One such a counter (pictured below) has a stags head armorial, and is classified as 'family unknown'; but as you have Canton armorial porcelain, you never know if this is a Parker counter! It was made in Canton in c1810.
(Kindly Donated by Rev Christopher Wood, Waddington, April 2021)