Spashett & Sons was a long-serving dealer in books, drygoods and stationary (This was back when people still wrote letters on actual paper. With pens.) I don't have any indication of who actually took the photographs, but I do suspect that it's one of the "& Sons" who saw that they were selling quite a few post cards along with the envelopes and bottles of ink and thought "why don't we make our own?" Like Harry Jenkins, Spashett was often on the spot during disasters and emergencies. They didn't do any studio work that I've seen.
Spashett's work is labeled in a variety of ways. They went by Spashett & Co. located at the Royal Arcade, (Suffolk Directory)
Terrace on London Road (G. S. Cook's Directory of Lowestoft and Kirkley 1882). Here they are listed as "Stationers and dealers in Fancy Goods"- not listed as a photographer.
"Spashett & Co'y" seems to be an older version.
I've also found an H. A. Spashett, Lowestoft about 1912.
Another version on the back of their cards is "Spashetts, Ltd." and "Copyright Photos by Spashett's, Lowestoft".