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It's a difficult question to wrap up in just a few lines, but the answer comes in the subtle differences in the marks and the knowledge of the style that David Crawford worked in. The hallmark, in this case there is just one, the Lion Passant, differs very slightly from those used at other assay offices, and the maker's mark, DC, is unique to David Crawford, and differs from any other 'DC' mark that was used by others around England.
The punches used, in this case, by Crawford and the Newcastle office were locally made, and though at a glance may appear the same as those used in, say, London, they are distinctly different.
With experience these differences stand out, much in the same way as a wine lover can instantly tell the difference between a Pinot noir and a Merlot (or in my case, a Big Mac and a Whopper!).