The full HEFCE policy can be found on their website alongside supporting documentation.
The HEFCE policy does not lay out any specific requirements for licensing. However, it does expect that articles are “…presented in a form that allows anyone with internet access to search electronically within the text, read it and download it without charge.”
It is advised that the Creative Commons Attribution, Non-commercial, No derivatives (CC-BY-NC-ND) license would meet this requirement. This is the most restrictive Creative Commons license. As such, use of any Creative Commons license can be used: in particular, other funder requirements for more open licensing (e.g., RCUK) will also meet HEFCE requirements.