The “round pounds”, which have been in circulation since 1983, can only be spent until midnight next Sunday.
However, they can still be paid into bank and building society accounts after that.
People are also urged to donate the coins to BBC Children in Need for Pudsey’s Round Pound Countdown.
They are being collected by banks and building societies, the Post Office, Boots, Greggs, Cineworld and Welcome Break.
The Royal Mint said 1.2 billion of the estimated 1.7 billion round pounds in circulation had been returned. However, despite some 500 million remaining, the process was “absolutely on track”. Many are thought to be lying in piggy banks and jars in people’s homes.
The Royal Bank of Scotland has said there will be no time limit on customers being able to pay in the old coins.
A total of £1.9 million worth of coins are being melted down every day in the Royal Mint’s furnaces to be reused in new coins. They are being replaced by 12-sided coins, which have been in circulation since March.
The change is because the old coins are among the most commonly faked currency, while the Royal Mint says the new one is the most secure coin in the world.
New security features include a hologram-like image that changes from a “£” symbol to the number “1” when the coin is seen from different angles. The coin also has micro-lettering and milled edges.
Meanwhile, Scottish banks said there would be no cut-off date for spending paper £10 notes following the debut of polymer versions.
A spokeswoman for the Committee of Scottish Bankers said: “As all Scottish notes are legal currency, they won’t be withdrawn from circulation in the same way as the Bank of England notes with a final date.
“Instead, the Scottish banks will withdraw their paper £5 and £10 notes from circulation as they are banked and polymer notes are issued. Any notes still in circulation will continue to be honoured and if you have any of these you can take them to your branch/bank for credit to your account.”