The recent increase in data and model scale for language model pre-training has led to huge training costs. In scenarios where new data become available over time, updating a model instead of fully retraining it would therefore provide significant gains. In this paper, we study the benefits and downsides of updating a language model when new data comes from new languages - the case of continual learning under language shift. Starting from a monolingual English language model, we incrementally add data from Norwegian and Icelandic to investigate how forward and backward transfer effects depend on the pre-training order and characteristics of languages, for different model sizes and learning rate schedulers. Our results show that, while forward transfer is largely positive and independent of language order, backward transfer can be either positive or negative depending on the order and characteristics of new languages. To explain these patterns we explore several language similarity metrics and find that syntactic similarity appears to have the best correlation with our results.