Computer-assisted (diagnostic) coding (CAC) aims to improve the operational productivity and accuracy of clinical coders. The level of accuracy, especially for a wide range of complex and less prevalent clinical cases, remains an open research problem. This study investigates this problem on a broad spectrum of diagnostic codes and, in particular, investigates the effectiveness of utilising SNOMED CT for ICD-10 diagnosis coding. Hospital progress notes were used to provide the narrative rich electronic patient records for the investigation. A natural language processing (NLP) approach using mappings between SNOMED CT and ICD-10-AM (Australian Modification) was used to guide the coding. The proposed approach achieved 54.1% sensitivity and 70.2% positive predictive value. Given the complexity of the task, this was encouraging given the simplicity of the approach and what was projected as possible from a manual diagnosis code validation study (76.3% sensitivity). The results show the potential for advanced NLP-based approaches that leverage SNOMED CT to ICD-10 mapping for hospital in-patient coding.