The Edward VIII halfcrown, dated 1937, will be auctioned by Noonans on May 26.
Edward abdicated before any coins bearing his name were issued.
Bradley Hopper, head of the coin department at Noonans, said: “Edward VIII abdicated in 1936 before any coins in his name were released into circulation in Britain.
“Patterns of each denomination had been prepared (all dated 1937) but at the time of the abdication, they had not yet received royal approval.
“After the abdication, the few coins which had been struck were locked away.”
At this time, the Royal Mint began work on coinage for George VI instead.
Mr Hopper said it remains unclear how any of Edward’s coins made it into private hands.
He said: “It is not known how the coins in private hands came to be in the public domain so opportunities to acquire any of these coins are very rare and we expect this coin to be keenly contested.”
A total of six pattern sets were struck, from five pounds to farthing, and of those, five complete sets are held.
Mr Hopper said: “Three belong to the Royal Mint Collection (one of which is on permanent loan to the British Museum), another is to be found in the Royal Collection, while the final complete set is to be found in within the famed Tyrant Collection.
“It seems most improbable that any of these will come to market in foreseeable future.”
The halfcrown up for auction comes from the final sixth set.
It is one of only two believed to be in private hands.
Mr Hopper said: “This was originally sold at auction in the USA in 1978 and has remained in the same collection for the past 40 years.”
Other coins from the set have appeared at auction in recent years.
A five-pound coin sold for $1.9 million in 2021 and a crown fetched $300,000 in January 2020.
The present halfcrown is of particular numismatic significance.
Mr Hopper said: “The effigy with the king makes a conspicuous break with almost 300 years of tradition.
“From the time of Charles II monarchs arranged their portraits so that they faced in the opposite direction to their immediate predecessor.
“Edward’s father, George V, had a left facing effigy, and so Edward’s should have faced to the right on his coinage.
“However, when the king sat for the engraver Humphrey Paget on the 28th April 1936, he presented the left side of his head, so that his fashionable side parting might be depicted.”
He described it as “A remarkable choice, which serves as a tangible reminder of Edward’s extraordinary reign, perhaps the most infamous of any British Monarch.”
