The plans for a European Health Data Space (EHDS) envisage an ambitious and radical platform that will inter alia make the sharing of secondary health data easier. It will encourage the systematic sharing of health data and provide a legal framework for it to be shared by Health Data Access Bodies (HDABs) based in each of the Member States. Whilst this promises to bring about major benefits for research and innovation, it also raises serious questions given the intrinsic sensitivity of health data. Fears concerning privacy harms on the individual level and detrimental effects on the societal level have been raised. This article discusses two of the main protective pillars designed to allay such concerns. The first is that the proposal clearly outlines several contexts for which a Health Data Access Permit (HDAP) should and should not be granted. The second is that a request for an HDAP must also be compliant with the GDPR (inter alia requiring a valid legal basis and respecting data processing principles such as ‘minimization’ and ‘storage limitation’). As this article discusses, in some instances the need to have a valid legal basis under the GDPR may make it difficult to obtain a data access permit, in particular for some of the commercially orientated grounds outlined within the EHDS proposal. A further important issue concerns the ability of HDABs to analyse the compatibility permit requests under the GDPR and relevant national law at both speed and scale.