Human culture is the result of a unique cumulative evolutionary process. The social transmission mechanisms underlying this process are still not fully understood. In particular, the role of language – another unique human behaviour – in social transmission is under-explored. In this first direct, systematic comparison of demonstration vs language-based social learning, we measured the transmission fidelity and cumulative improvement of an action sequence whose objective was to extract a reward from a box. Participants were organised in transmission chains, and each of them either watched a model demonstrate an action sequence or listened to verbal instructions to produce the action sequence. In order to explore imitation and overimitation, the sequences included actions that were causally relevant or irrelevant, respectively, to extracting the reward. We explored these effects in transmission adults and in 6 to 8-year-old children. Overall, we found more retention of causally relevant than irrelevant actions. More interestingly, children (but not adults) retained more causally irrelevant actions under verbal instruction, but more causally relevant actions under demonstration. Cumulative cultural evolution produces sophisticated, complex behaviour whose function may not be obvious. By promoting the retention of behaviour even when its function is not understood, specifically in children, language may play a supportive role in cumulative cultural evolution.