Found an interesting article by M. Mapleton in the February 1971 edition of Coin Monthly, on the general topic of die No's under dates. Specifically mentioned at points in the article are the die numbers under 1863 pennies and die letters on 1862 halfpennies. These remain as big a mystery today as they were nearly 50 years ago.
According to the article, the Royal Mint kept no records as to why the die numbers were used, and we are just left with the theories of either experimentation to test die wear or a means of identifying an individual operative.
Anyway, here is the article in its entirety for anyone interested. They're not brilliant photos, so apologies for that, but they are readable:-