Abstract Excess hazard modelling is one of the main tools in population-based cancer survival research. Indeed, this setting allows for direct modelling of the survival due to cancer even in the absence of reliable information on the cause of death, which is common in population-based cancer epidemiology studies. We propose a unifying link-based additive modelling framework for the excess hazard that allows for the inclusion of many types of covariate effects, including spatial and time-dependent effects, using any type of smoother, such as thin plate, cubic splines, tensor products and Markov random fields. In addition, this framework accounts for all types of censoring as well as left truncation. Estimation is conducted by using an efficient and stable penalized likelihood-based algorithm whose empirical performance is evaluated through extensive simulation studies. Some theoretical and asymptotic results are discussed. Two case studies are presented using population-based cancer data from patients diagnosed with breast (female), colon and lung cancers in England. The results support the presence of non-linear and time-dependent effects as well as spatial variation. The proposed approach is available in the R package GJRM.