Then there's the threat to the NHS

The trade treaty being negotiated between the USA and the EU specifically excludes the NHS and similar public undertakings from the competition rules which everybody is so exercised about. If the UK leaves the EU, and wishes to negotiate its own treaty with the US, then this is likely to be on terms more favourable to the US as the stronger party. The NHS would thus be more open to privatisation.

The TUC has found other threats: https://www.tuc.org.uk/sites/default/files/brexit-TheNHS2.pdf