Answer:
If by "banked" you mean deposited in a savings account or exchanged for modern currency, no. All predecimal coins have long been demonetised and are no longer legal tender.
Even demonetised decimal coins such as the Half New Penny, the old style 5 Pence, 10 Pence and 50 Pence coins, might only be accepted by a bank from an account holding customer and exchanged for coins of an equivalent value, but banks are under no obligation to do this.
If you have predecimal coins that you want to get rid of, and they are in good condition, you may be better off taking them to a coin dealer.