This happened with more than one letter. For instance the Scots language had a letter yogh (https://en.wikipedia.org/wiki/Yogh), which was written somewhat like a rounded "3" but lower on the line. Early printers had only the characters of the English language, and since this character looked like a hand-written z, that is what they used in its place. Hence the name "Menzies" is pronounced "Ming-is", since that isn't actually a z.

Welsh suffered more: it used to be full of "k"s. When the first Welsh Bible was printed, the English printer did not have enough "k"s, and substituted "c", and the language now does not use "k" at all. Apparently the printer's note on the matter still exists.

Just to expand on this:

"ye" in "ye Olde mill" is actually just "the" but originally "þe"/"þee". The first printing presses to England were imported from Germany, which never used þ, so printers used something that looked sorta similar, thus "y".

"Ye" was a different word, the 2nd person non-formal version of "you" (which was historically formal: see-Shakespeare and how he played with "ye" and "you"). Thorn was on its way out along with "ð" both of which were in Middle English. The sounds didn't leave English, but we merged it into one letter cluster "th" (think "that" and "the", which have different th sounds).