The medal, which also shows a third clasp for earlier service in Egypt during the French Revolutionary Wars, was found inside an old tobacco tin.
It was presented to the surgeon Thomas Robertson (c.1774-1867), who joined the Royal Navy in 1793.
This was the year that Britain’s war against Revolutionary France began and Robertson kept a diary from then until his death.
He was described as ‘an observant world traveller full of curiosity ingenuity and Directness’ and he was said to be ‘as much a sailor as a Surgeon’.
His journals, which he began just to record his first voyage for the benefit of his family, turned into arguably the most complete history of a British naval surgeon’s career of this period.
The medal is being offered for sale by Gorringe’s in East Sussex on April 14 with an estimate of £10,000-£15,000.
James Hancox, who found the medal after it was brought into the saleroom, said: “To handle a Naval General Service Medal with a Trafalgar clasp is exciting in itself, but the addition of the Sirius clasp and the full and fascinating career of the recipient, truly makes this a once in a lifetime find.
“We believe it to be just one of ten that are known to exist and there is much excitement about the discovery.
“Robertson had a long career in the Royal Navy and was highly regarded by those who sailed with him.
“He made a number of voyages without facing action but had to deal with all manner of diseases including Yellow Fever, scurvy, and The Plague.
“At Trafalgar he was on board HMS Sirius, a 36-gun fifth rate frigate. She was close to the cost and was the ship that signalled to the rest of the fleet when the combined French and Spanish fleets set sail for battle.
“Sirius was so close she had to quickly get out of the way to avoid being taken. She was the ‘eyes of the fleet’ and while she wasn’t directly involved in the action, took the legendary ship Temeraire in tow afterwards.
“The following year, still under the captain William Prose, Sirius distinguished herself after spotting a French flotilla in the mouth of the River Tiber in Italy.
“Out numbered and outgunned she attacked and after wo hours fighting took the French ship Bergere.
“Nine of Sirius’ crew were killed with 20 injured and Robertson was kept busy dealing with the injuries.”
Robertson married Elisabeth Harvie in 1811 and they settled in Gillingham in Kent and had five children.
He worked as a surgeon until 1828 in various roles and died in 1867. He had been born the son of a West Lothian farmer and trained for his career in Tranent and at Edinburgh University.