Teaser 2915: £sd

From The Sunday Times, 5th August 2018 [link]

50 years ago, the coins in circulation were the halfpenny (1/2d), penny (1d), threepenny bit (3d), sixpence (6d), shilling (12d), florin (2 shillings) and half crown (2 shillings and sixpence).

One day, having at least one of each of the above coins, I decided to bank them.

The cashier set out the coins in separate piles, checked them (discovering that the number of coins in each pile was a square), and gave me exactly a 10-shilling note in exchange.

If I told you how many different numbers of coins were in those piles, you should be able to work out the numbers of each coin.

In the order half crown down to halfpenny, how many coins of each type were there?