Fifteen taxa were found in a comprehensive study of British Silurian stromatoporoids using new and museum samples. The approach towards systematics adopted here is to accept that the taxa are Phylum Porifera, and are hypercalcified sponges, noting that there is not proof of a sponge affinity in one taxon, Lophiostroma schmidti, included in this systematic account. Below the phylum level, however, the absence of spicules makes classification of stromatoporoids a problem that lacks evidence to resolve it. Thus the taxa are presented as a list of lowest-level taxa, that may or may not be equivalent to biological species. No grouping into orders and families is presented, in recognition of the lack of evidence of their groupings. No new taxa, at either traditional genus or species levels were discovered in the sample set of new material and museum samples. We surmise that the range of taxa of British and Irish Silurian stromatoporoids is stable and discovery of new species considered unlikely. Illustrations of taxonomic features is provided here together with notes on each taxon. For formal taxonomic descriptions, reference is made to published work at the level of traditional genus definitions in relevant chapters of the Treatise on Paleontology, Part E (Nestor 2015, Stearn 2015a, Stock 2015, Webby, 2015), and traditional species descriptions from Nicholson (1886-1892) and Mori (1969a & 1970) which include all the taxa found in this study. From Mori’s (1969a & 1970) work, growth forms of stromatoporoids of Gotland are included. In order to achieve accessibility for the reader, taxa descriptions from those publications are provided as quoted text linked to specific pages, that can be compared with the illustrations. Discussion is provided where appropriate. Older literature descriptions give precise descriptions of the traditional species, but they use older terminology that has been updated in the 2015 Treatise volume, so it is necessary for the reader to appreciate some outdated terms, particularly “coenosteum” and “pseudozooidal tubes” derived from the earlier times when stromatoporoids were interpreted as belonging to the Cnidaria phylum. Within the quoted text, additional notes are added by us, in square and ornamental brackets, where appropriate. Two taxa incompletely described in the UK Silurian stromatoporoid literature are included in this atlas. They are Labechia rotunda Johnston (1915) and Labechia scabiosa Nicholson (1886-1892), the holotypes of which are in the NHM and are indeed the only samples of these taxa. Both taxa were presented by these authors using only hand specimens, without thin section study, surprising considering the high research calibre of both Johnston and Nicholson in their era. Both taxa were considered by Mori (1970) to be invalid, a conclusion we agree with, but these taxa are illustrated here for the first time. The following taxa have been described: - Labechia conferta (Lonsdale) - Labechia rotunda Johnston 1915 - Labechia scabiosa Nicholson 1886-1892 - Lophiostroma schmidti (Nicholson) - Ecclimadictyon macrotuberculatum (Riabinin) - Ecclimadictyon astrolaxum (Nestor) - Petridiostroma simplex (Nestor) - Petridiostroma linnarsoni (Nicholson) - Actinostromella vaiverensis (Nestor) - Araneosustroma fistulosum Lessovaya 1970 - Densastroma pexisum (Yavorsky) - Plectostroma intertextum (Nicholson) - “Stromatopora” venukovi Yavorsky - Eostromatopora impexa (Nestor) - Simplexodictyon yavorskyi (Nestor) - Syringostromella borealis (Nicholson) - Parallelostroma typicum (Rosen)