New 12-sided £1 coins are already being put on sale online with some "extra rare" coins being offered for hundreds of pounds.
The Royal Mint’s new coin, which is described as the most secure in the world, went into circulation in the UK on Tuesday.
It has a gold-coloured outer ring and silver in the middle and includes high-tech features including a hologram.
But just hours after the first bags of coins were delivered to banks up and down the country, new £1 coins began appearing for sale online at several times their face value.
People have already bid over £100 on online auction site eBay for particular coins, including one 12-sided pound coin which appears to be dated 2015.
For uncirculated coins marked with the year 2016, some sellers are charging hundreds of pounds and another person is asking £2,500 for a coin which has “slipped through the net”.
Another seller is selling an unopened bag of 500 £1 coins allegedly “straight from the Royal Mint” and dated 2016 for £849.
The Royal Mint in Llantrisant, South Wales, has been making millions of the new £1 coins per day in the run-up to the launch.
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 production of the new coins follows concerns about round pounds being vulnerable to sophisticated counterfeiters.
Around one in every 30 £1 coins in people's change in recent years has been fake.