Several months advance notice is provided before a coin is demonetised (i.e. it is no longer legal tender). However, once a coin has been demonetised, banks are under no obligation to accept them. Nevertheless, many banks will accept demonetised coins from members of the public providing they have a bank account with them. Policy may vary from bank to bank, and some may charge a handling fee.
After decimalisation in 1971 One Shilling and Two Shilling coins were used as 5p and 10p respectively because the new coins were assigned the same size and value as their older counterparts. It was only when smaller 5p and 10p coins were introduced during the early 1990s that any remaining Shillings finally disappeared from general circulation.
Bank of England banknotes are treated differently to coins inasmuch as they retain their face value for all time, therefore the BoE will always exchange withdrawn notes (such as the Elgar £20 which is due to be withdrawn on 30th June). Again, other financial institutions are under no obligation but may do so for recently withdrawn banknotes.