It has been a long time since coins were made by hand in England (the technical term is hammered coinage, to distinguish it from the modern machine-made type).
The language associated with it is as obsolete as the technique. Coin blanks were called flans. This is the same French word as the one we use in Britain for an open tart (in the USA for a custard baked with a caramel glaze), which can be traced back to the old Germanic flado, a flat cake; we once had a relative, flawn, for a type of cheesecake or pancake, which led to the long-defunct proverb “as flat as a flawn”.
The flan was placed on an anvil called a pile. This is from Latin pila, a pillar, and is a close relative of the words for things piled in a heap and piles driven into the ground to support a structure. The anvil got that name because it was a short upright iron pillar, usually driven into a wooden base.
The coiner put the flan on the pile, placed a punch called a trussell on top and hit it with a hammer. The top of the pile and the bottom of the trussell were engraved with the designs for the two sides of the coin, which were thereby transferred to the flan.
Trussell is from the same source as modern French trousseau and our truss, both at first meaning a bundle or package, though it isn’t obvious how it came to be used for a die punch.