The rarest is the Kew's Garden 50p, which was designed to mark the 250th anniversary of the gardens in 2009.
A rare “mule” 20p coin dating from 2008 has fetched more than £60 at auction.
The coin was minted without a date due to an error and quickly became a sought-after collector’s item.
Prior to November 2008, the date on 20p coins would be found on the tail side.
However, the Royal Mint switched it so that the date would now be next to the Queen’s head.
But a mistake led to the old format being used on the Queen’s side and the new format being used on tails.
As a result, the first batch of British coins with no date on them was released into circulation for the first time in more than 300 years.
It is believed that around 250,000 20p coins minted in November 2008 entered circulation with no date.
After attracting 14 bids, the 20p coin sold for £61.09.
The coin was among a number of rare Royal Mint pieces which are still in circulation in the UK.
The rarest is the Kew’s Garden 50p, which was designed to mark the 250th anniversary of the gardens in 2009.
Only 210,000 coins were ever minted with this design, and they now sell for an average of £156.25.
Incredibly, one seller managed to get more than £700 for one of the 50p coins when they sold it on eBay.
The other rarest coins largely stem from the 2011 Olympics, with the wrestling, football and judo coins among the most valuable.
Only 1.1million of each of these coins were produced, and they are now worth around £20 each.
Also highly valuable are the Flopsy bunny and Peter Rabbit designs which were produced in 2018.
These coins - 1.4 million of which were minted - depict the characters from Beatrix Potter’s novels and celebrate the life of the English writer and these sell for around £5.
In 2019, 500 million coins were produced, with three new 50p designs.
These included one of Arthur Conan Doyle’s Sherlock Holmes, Paddington Bear at St Paul's Cathedral and the Tower of London.
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