"I will fetch you a toothpicker now from the furthest inch of Asia"
Much Ado About Nothing Act II, Scene 1
"He seems to be more noble in being fantastical;
A great man, I’ll warrant;
I know by the picking on’s teeth"
The Winter's Tale Act IV, Scene 4
The first quotation implies that toothpicks were imported into Britain. Certainly the royal family had theirs imported as they show up in import lists alongside ear picks.
Toothpicks probably became a fashionable item amongst the nobility and were just as much about showing off their wealth as keeping their teeth clean.
In 1570 Elizabeth I received a gift of six gold toothpicks whilst King James IV of Scotland had two gold toothpicks which he wore on a chain around his neck. His son, James V, even ordered a special silver case for his toothpicks.
Poor Tudors must have just found a sliver of wood to use as a toothpick or even, according to an etiquette book of 1577, their knife or finger!
Try a book on toothpicks