Above showing close-up of print below.

Above engraving, date unknown, artist I believe is James Adam.

Admiral Rodney, Sandwich - c.1785. A very rare innkeeper's token. Rory Kehoe who sent the above image of the coins doubts that this pub was called the Admiral Rodney before 1760 at the earliest, for the simple reason that not many people outside the Royal Navy would have heard of George Brydges Rodney (1718 to 1792) until the Seven Year War (1756 - 1763) George Brydges was promoted to Rear Admiral in May 1759 so it's reasonable to think that the pub in Sandwich was called something else before changing its name in the 1760s/70s. Towards the end of a very successful career, Rodney's greatest victory was at the Battle of Saintes in 1782, when he utterly defeated a larger French fleet off the coast of Dominica. It's quite possible then, that the Admiral Rodney pub didn't get it's new name until as late as the mid 1780s then, when Rodney was being feted as a national hero. Many publicans issued tokens for food and drink, sometimes in part-payment of wages, until this practice was largely made illegal in the Truck Act of 1831.

Further research sent to me by Debi Birkin shows the following:-

Above photo showing a copper medal showing the bust of Admiral Rodney wearing a cocked hat, the reverse show HMS Sandwich. This coin actually commemorates Rodney's success at the battle of Cape St Vincent in 1780 and HMS Sandwich was the flag ship of Rodney's fleet.

Admiral George Rodney was commander of the ship HMS Sandwich. The Sandwich was built at Chatham in 1759, and participated in the Battle of Cape St Vincent in 1780, where she served as Admiral Rodney's flagship.

The medal can be dated at 1780/1. From 1790 she was on harbour service. Richard Parker was hanged onboard the Sandwich off Sheerness in 1797 after the Mutiny of the Nore.

The Sandwich was broken up in 1810. There are several Admiral Rodney ships medals that commemorate service on different ships under his command. eg;. Admiral Rodney HMS Formidable medal date c1782 commemorates the battle of Saints during the American war of independence when Rodney beat the French in the West Indies.

They actually don't appear to be as rare as first thought, and I now doubt they had anything to do with the pub at all.