The coins will lose their legal tender status on Sunday. After this date, shops and restaurants should no longer accept them.
"Retailers are under no obligation to accept the round £1 coin from customers and should not distribute the round £1 coin after October 15".
Chief executive and deputy master of the Royal Mint Adam Lawrence said: "The round pound has been in circulation for over 30 years but, as the deadline approaches, we are keen to encourage everyone to track down their final coins and use them".
Roughly 500 million old pound coins are thought to still be in circulation in the United Kingdom, but as of midnight on Sunday businesses can stop accepting them.
Poundland (the British version of one dollar shops) said more than 850 of its United Kingdom stores would continue accepting the coins until October 31. People may also find they can still hand in the old £1 coins at the Post Office after this date.
"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 Royal Mint created the new coin in an attempt to combat fraud, with three per cent of the old coins - equivalent to £45 million - deemed to be counterfeit.
While banks and Post Offices will continue to accept your old pound coins, money saving expert-type Martin Lewis explains: "Carting a bag of coins to the bank is a real faff - particularly if there isn't a branch near you".
One pound coins were first launched on 21 April 1983 to replace £1 notes.
The new coin, of which 1.5 billion copies have been made, is "the safest in the world", said Kevin Clancy, director of the Royal Mint Museum.
The Post Office is also taking part in "Pudsey's round pound countdown" - collecting old round £1 coins for BBC Children in Need.
If you do not want to risk being caught out though, bear in mind that shops are not obliged to accept your old round pound after October 15, so it would be wise to offload your old coins by banking, spending or giving them to charity before then.