If you use hammers to shape metal directly (no punches or other intermediate devices) it is important to have a face that nearly matches the finished surface curvature, (smaller never larger), and a handle at a position so that you can get a good swing. It is also sometimes necessary to have the contact surface quite a long way from the handle axis because something else gets in the way. As there is a wide range of surface radii, handle positions, and extensions, trades like silversmithing and panel beating are very hammer-rich. And of course, they also need all the other types for closing rivets, using with cold chisels, driving pins, pegs, and nails, and punches. And if they also do repousse work or chasing, they will need two or three sizes with wide flat faces, and very springy handles, to keep up the continuous steady vickers-gun on each of at least 30 punches in turn.
So, the answer is a clue to the trade.
Warrington was a centre for steel wire production, much of it for winding gear in coal mines. So what was a Warrington Pattern hammer intended for, originally?
Cheers, Tim