Queen Anne seems to have been the last of the English sovereigns who actually performed the ceremony of touching. Dr. Dicken, her Majesty's sergeant surgeon, examined all the persons who were brought to her, and bore witness to the certainty of some of the cures.
The practice of the Royal Touch was put to a stop in Great Britain by King George I, but continued to be practiced for a time by the various Royals in France.
Here we have an engraving of the gold touch-piece of Charles II, obverse and reverse; and the identical touch-piece, obverse and reverse, given by Queen Anne.
It is my belief that everyone of the 18th Century would be familiar with the 'King's Evil' and the superstition of how to cure it, even though the Royal Touch was no longer in fashion by 1780. Older folks would be familiar with it for certain, even if it was just by having heard it from parents or grandparents.
In 1768, there was an essay written by mr. John Morley Esq. about Scrofula and the King's Evil entitled, appropriately enough: "An essay on the nature and cure of scrophulous disorders, vulgarly called the King's evil"
I especially enjoy the author's remark on the cover, "Facts are Stubborn Things", which might also be stated, "Superstition is the Enemy of Reason".