The Bank of England has said it will withdraw legal tender status of paper £20 and £50 notes on September 30 next year.
It urged anyone who has them to spend or deposit them at a bank or Post Office.
There are about £9 billion ($12.13bn) worth of paper £20 and £15bn worth of paper £50 notes still in circulation.
Their withdrawal will mean polymer equivalents will become the only notes of this denomination in legal tender.
Although the current versions will become obsolete next year, the BoE said people would still be able deposit them into their account.
Some Post Office branches might accept them as payment for goods and services or as a deposit to an account accessed through the Post Office.
BoE chief cashier Sarah John said the decision was made for security reasons – with the new notes "more difficult to counterfeit" – and that it would cause the public little inconvenience.
"The polymer £20 featuring the artist J.M.W. Turner and the polymer £50 featuring the scientist Alan Turing are now in wide circulation," she said.
The new polymer £20 was issued on 20 February, 2020, and the £50 note on 23 June this year.
These notes complete the BoE’s first polymer series. The introduction of such banknotes allows for new security features, which make them more difficult to counterfeit. The notes are resistant to dirt and moisture and so remain in better condition for longer. The notes also have tactile features that allow the blind and the partially-sighted to use them more easily.