There are essentially two different ways an inscription can be placed onto the edge of a coin. The old-fashioned way is having a collar die with a lettered edge; the lettering is thus part of the die set and imparted when the entire coin is created, all at once. In this situation, there is usually a "right way" and a "wrong way" for the collar die to be inserted, and thus the possibility of "wrong way up edge" mint errors.
Edge-lettered collar dies are cumbersome and expensive, so for modern circulation coins, they use a different technique: applying the edge in a separate stage, either before or after the coin is struck. For British coins, this is "before", being applied to the blanks prior to striking the obverse and reverse. For American "golden dollars", I believe it is "after" the coin is struck. But either way, the separate stage of the process means the coins can and do get flipped around any and every which way, making the final product usually have a 50:50 distribution of orientations. Most collectors do not even consider the different edge orientations to be separate "varieties".
It should perhaps be noted that for British Proof coins,
The Royal Mint uses an edge-lettered collar die. So the proof versions of the pound coin might indeed have a "wrong way up edge error". But circulation coins do not.
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