The process of leaving the European Union (EU) will have profound consequences for health and the National Health Service (NHS) in the UK. In this paper, we use the WHO health system building blocks framework to assess the likely effects of three scenarios we term soft Brexit, hard Brexit, and failed Brexit. We conclude that each scenario poses substantial threats. The workforce of the NHS is heavily reliant on EU staff. Financing of health care for UK citizens in the EU and vice versa is threatened, as is access to some capital funds, while Brexit threatens overall economic performance. Access to pharmaceuticals, technology, blood, and organs for transplant is jeopardised. Information used for international comparisons is threatened, as is service delivery, especially in Northern Ireland. Governance concerns relate to public health, competition and trade law, and research. However, we identified a few potential opportunities for improvement in areas such as competition law and flexibility of training, should the UK Government take them. Overall, a soft version of Brexit would minimise health threats whereas failed Brexit would be the riskiest outcome. Effective parliamentary scrutiny of policy and legal changes will be essential, but the scale of the task risks overwhelming parliament and the civil service.