Instrumental variable (IV) analysis is an increasingly popular tool for inferring the effect of an exposure on an outcome, as witnessed by the growing number of IV applications in epidemiology, for instance. The majority of IV analyses of time-to-event endpoints are, however, dominated by heuristic approaches. More rigorous proposals have either sidestepped the Cox model, or considered it within a restrictive context with dichotomous exposure and instrument, amongst other limitations. The aim of this article is to reconsider IV estimation under a structural Cox model, allowing for arbitrary exposure and instruments. We propose a novel class of estimators and derive their asymptotic properties. The methodology is illustrated using two real data applications, and using simulated data.