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On British coinage:
The title Fidei Defensor abbreviated to F.D. (Defender of the Faith) occurs for the first time on the British coinage under George I.
The earliest example is from the very beginning of his reign, in 1714.
"1 Guinea - George I 1st portrait". Source: Numista
The inscription appears frequently on coins from here on. For example, a 1722 silver shilling reads (obverse):
GEORGIVS D G M BR FR ET HIB REX F D (translation: George I by the Grace of God King of Great Britain, France and Ireland, Defender of the Faith).
Image source: 1722 Great Britain Silver Shilling Coin George I, ebay
However, not all coins during his reign bore this inscription: see this 1722 farthing, for example.
The terms "dei gratia" or "gratia dei" (followed by "rex") on coins can be dated back much earlier, to Anglo-Saxon times. For example, it was used by Coenwulf of Mercia (reigned 796 to 821). It was also used by the Normans and their successors, though not on all coins.
Note
A paragraph in the Wikipedia page for King James VI & I is somewhat poorly phrased in that it implies James used Defender of the Faith on coins. However, the sources cited (Willson 1967 and Croft 2003) do not say that; rather, they are referring to the use of the title King of Great Brittaine (which was controversial). Nor can I find any James VI or I coins with D.F..