Rush is on to offload old round pounds ahead of Sunday's deadline
Shoppers have only this weekend left before the old round pound rolls out of general circulation - with hundreds of millions of coins still to be handed in.
While some stores will let people continue spending their round pounds for a limited extra period, the coins will no longer be legal tender from midnight on Sunday.
Around 400 to 450 million old round coins are still lying around in wallets, pockets and piggy banks up and down the country, after people have been returning old pound coins at a rate of up to 60 million per week.
NatWest said it has seen a rush of people offloading their old round pounds.
It said in the in the first week of October there was an 80% increase in the number of £1 coins being deposited at NatWest branches, with over 5.5 million pound coins deposited through coin machines, an increase of two million coins compared with the normal weekly average of just over three million.
Carl Foster, head of coins at NatWest, said: "We've seen a large increase in the number of coins being brought into branch in the last couple of weeks as customers empty their piggy banks not just of round pound coins but of all their loose change."
NatWest said the total number of coins deposited rose to 34.5 million in the first week of October, compared to just over 24 million coins received over a week in September.
Major banks and building societies have said they will continue to accept deposits of the old round pound after the deadline on Sunday October 15.
People can also deposit them into any of their usual high street banks through the Post Office after this date.
Martin Kearsley, banking services director at the Post Office, said: "Thanks to an agreement with all UK high street banks, everyone can deposit old pound coins into their usual high street bank account at their local Post Office branch."
Some major stores have said they will give shoppers an extra window of opportunity to spend up their old pound coins after October 15.
Iceland and Poundland have said they will continue to accept the old round pound until October 31, while Tesco has said it will continue accepting the old-style coins for a week after the October 15 deadline.
One pound coins were first launched on April 21 1983 to replace £1 notes. The Royal Mint has produced more than two billion round pound coins since that time.
The new 12-sided pound coin, which resembles the old threepenny bit, entered circulation in March and boasts new high-tech security features to thwart counterfeiters.
The production of the new coins follows concerns about round pounds being vulnerable to sophisticated counterfeiters. Around one in every 30 old-style pound coins in people's change in recent years has been fake.
Trade bodies say the industry has been working hard to update machines in time for the deadline. But there may be some cases where people find they are caught short.
The British Parking Association has said it is confident that the majority of parking machines are ready or will be ready to accept the new £1 coin, while the Automatic Vending Association (AVA) said it believes all machines owned by its members are now accepting the new coin.