In recent years, the number of machine learning (ML) technologies gaining regulatory approval for healthcare has increased significantly allowing them to be placed on the market. However, the regulatory frameworks applied to them were originally devised for traditional software, which has largely rule-based behaviour, compared to the data-driven and learnt behaviour of ML. As the frameworks are in the process of reformation, there is a need to proactively assure the safety of ML to prevent patient safety being compromised. The Assurance of Machine Learning for use in Autonomous Systems (AMLAS) methodology was developed by the Assuring Autonomy International Programme based on well-established concepts in system safety. This review has appraised the methodology by consulting ML manufacturers to understand if it converges or diverges from their current safety assurance practices, whether there are gaps and limitations in its structure and if it is fit for purpose when applied to the healthcare domain. Through this work we offer the view that there is clear utility for AMLAS as a safety assurance methodology when applied to healthcare machine learning technologies, although development of healthcare specific supplementary guidance would benefit those implementing the methodology.