People have just one week remaining to spend their old £1 coins before businesses can refuse to accept them.
From 16 October, the round £1 coin will no longer be legal tender, having been replaced by a new 12-sided version earlier this year.
It will still be possible to deposit the old coins at most high street banks and the Post Office after that date.
About 1.2 billion coins have so far been returned, but an estimated 500 million are still in circulation.
Adam Lawrence, chief executive of the Royal Mint, said: “As the deadline approaches, we are keen to encourage everyone to track down their final coins and use them.”
Ten places to find your old £1 coins
New £1 coin’s ‘hidden’ security feature
The Royal Mint introduced the new £1 coin on 28 March to help crack down on counterfeiting, with one in 30 of the old version estimated to be fake.
It was described as the “most secure coin in the world”, with a string of anti-counterfeiting details, including material inside which can be detected when electronically scanned by coin-counting or payment machines.
Nevertheless, it has faced some problems since its introduction.
A “small number” of coins put into circulation were found to be faulty, while some ticket and vending machines, as well as shopping trolleys, were unable to take it.
The AA reported in July that more than one in five UK councils had not converted all their parking ticket machines to accept the new coin.
The Royal Mint said some businesses waited until July to upgrade machines – once there were more new pounds in circulation than old ones.
Businesses were warned by the Treasury last year that they would need to update their machines and the Royal Mint says all “coin handling equipment should be able to accept the new £1 coin” from 16 October.
Efforts to phase out the old £1 coin have also been hampered by companies who returned the new 12-sided replacement by mistake.
Banks are encouraging customers to return their old coins as soon as possible and not to wait until after they cease to be legal tender.
The Post Office said customers could continue to deposit them into any of their usual high street bank accounts “until further notice”.
The new £1 coin: Vital statistics
Thickness: 2.8mm – thinner than old coin
Weight: 8.75g – lighter than old coin
Diameter: 23.43mm – larger than old coin
Number to enter circulation: 1.5 billion – about 23 per person. Old £1 coins will be melted down to make new ones
Outer ring: gold-coloured, made from nickel-brass
Inner ring: silver-coloured, made from nickel-plated alloy