It has been argued that human-centred security design needs to accommodate the considerations of three dimensions: (1) security, (2) usability and (3) accessibility. The latter has not yet received much attention. Now that governments and health services are increasingly requiring their citizens/patients to use online services, the need for accessible security and privacy has become far more pressing. The reality is that, for many, security measures are often exasperatingly inaccessible. Regardless of the outcome of the debate about the social acceptability of compelling people to access public services online, we still need to design accessibility into these systems, or risk excluding and marginalising swathes of the population who cannot use these systems in the same way as abled users. These users are particularly vulnerable to attack and online deception not only because security and privacy controls are inaccessible but also because they often struggle with depleted resources and capabilities together with less social, economic and political resilience. This conceptual paper contemplates the accessible dimension of human-centred security and its impact on the inclusivity of security technologies. We scope the range of vulnerabilities that can result from a lack of accessibility in security solutions and contemplate the nuances and complex challenges inherent in making security accessible. We conclude by suggesting a number of avenues for future work in this space.