As I kind of expected, the identity of this animal was revealed very quickly. This is the Cambrian mollusk Yochelcionella daleki, named after the most popular science fiction villains ever to be constructed from an upturned dustbin and a toilet plunger. And to be honest, anyone that knew me and knew that there was such an animal could have probably expected it to make an appearance here sooner or later. The high conical shell and the lateral 'snorkel' (which would have functioned in the living animal to expel water drawn in over the gills) distinguish it as Yochelcionella while Y. daleki is distinguished from other Yochelcionella species by its closely spaced rings and overall profile.
Yochelcionella is classified in the Helcionelloida, an assemblage of small mollusks that were found in the Cambrian and Ordovician. Helcionelloids are in turn one of the groups of mollusks referred to as 'monoplacophorans'. 'Monoplacophorans' have a small, undivided, generally cap-shaped shell and are essentially defined by their lack of the derived features of other molluscan 'classes'. As a classic negative grouping, 'monoplacophorans' have never been regarded as holophyletic. The uniting features of helcionelloids, such as a certain degree of lateral compression and an endogastric (directed backwards) shell, are also fairly plesiomorphic and the monophyly of helcionelloids is also suspect. The term 'monoplacophoran' is most commonly used in relation to the living species such as Neopilina galatheae; however, these species belong to a group called Tryblidiida characterised by serially-repeated organs and an exogastric (forward-directed) shell that is probably not closely related to helcionelloids.
Recent studies of mollusc phylogeny have recognised a clade uniting gastropods, scaphopods and cephalopods with the latter two more closely related (e.g. Wilson et al., 2010; the inclusion by that study of the shell-less caudofoveates in this clade has not been proposed elsewhere on morphological grounds but the remaining relationships have been). Many authors have regarded the 'helcionelloids' as representing the ancestral morphology of this clade. Yochelcionella and the related Eotebenna in particular have been suggested to be potentially connected to the origins of scaphopods and cephalopods (Peel, 2006); in contrast, Parkhaev (2002) classifies all 'helcionelloids' as early gastropods (albeit mostly stem taxa, so it kind of comes down to your definition of a 'gastropod'). Unfortunately, suggested relationships of helcionelloids to other molluscs are largely based on comparison of overall morphology and stratigraphy; because helcionelloid shells are generally small and fairly undistinguished, they preserve few characters for more detailed formal analyses.
Parkhaev, P. Y. 2002. Phylogenesis and the system of the Cambrian univalved molluscs. Paleontologicheskii Zhurnal 2002 (1): 27-39.
Peel, J. S. 2006. Scaphopodization in Palaeozoic molluscs. Palaeontology 49 (6): 1357-1364.
Runnegar, B., & P. A. Jell. 1976. Australian Middle Cambrian molluscs and their bearing on early molluscan evolution. Alcheringa 1 (2): 109-138.
Wilson, N. G., G. W. Rouse & G. Giribet. 2010. Assessing the molluscan hypothesis Serialia (Monoplacophora + Polyplacophora) using novel molecular data. Molecular Phylogenetics and Evolution 54 (1): 187-193.