Two thirds of the pounds still in circulation are expected to be spent by the end of the weekend to give shops a major windfall.
"All round £1 coins should have been banked".
Deputy master of The Mint, Adam Lawrence, said: "The round pound has been in circulation for over thirty years but, as the deadline approaches, we are keen to encourage everyone to track down their final coins and use them".
It follows a similar announcement by discount retailer Poundland, which will be accepting round pounds until October 31.
Despite the 12-sided coins being introduced in March to facilitate the phasing out of the old coins, some retailers have said they will continue to accept the coins.
However, some retailers have faced criticism over the change to the new 12-sided pound coins.
The hour of reckoning for the old pound coins is very almost upon us - they are just days away from being cast into the empty void of futility.
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"This deadline is going to be a challenge given that multiple retailers have made a decision to be more flexible and continue to accept the old £1 coin from shoppers after 15th October", he said.
The replacements are not yet accepted in some shopping trollies.
As the deadline looms for Brits to empty their pockets and homes of the much-loved round £1 coins, Poundland has today announced that it will be the first retailer in the country to accept the old coins after they are taken out of circulation on 15 October.
"They can do this even after 15th October".
The old coins may stop being legal tender at midnight on Sunday, but they can still be traded in for new ones at the Post Office or your bank's local branch.
The Post Office is also taking part in Pudsey's round pound countdown - collecting old round £1 coins for BBC Children in Need.