Since nobody else chose to elaborate on the connection between Hanseatic League and sterling silver, I will.
The members of the Hanseatic League each had trade outposts in Britain. There were two main groups: The Easterlings and the Westerlings. Each had a silver coinage of such dependable value that there arose a demand for it, and the phrase "Pound Sterling" became current.
I checked encyclopedia and got information that appears to conflict with what I read in Widener Library so many years ago. It gives much earlier date than Hanseatic League.

ENCYCLOPÆDIA BRITANNICA

pound sterling
the basic monetary unit of Great Britain, divided (since 1971) decimally into 100 new pence. The term is derived from the fact that, about 775, silver coins known as "sterlings" were issued in the Saxon kingdoms, 240 of them being minted from a pound of silver, the weight of which was probably about equal to the later troy pound. Hence large payments came to be reckoned in "pounds of sterlings," a phrase later shortened to "pounds sterling." After the Norman Conquest the pound was divided for accounting purposes into 20 shillings and into 240 pennies, or pence. In medieval Latin documents the words libra, solidus, and denarius were used to denote the pound, shilling, and penny, which gave rise to the use of the symbols £, s., and