The HEFCE/REF exception is not to the deposit requirement but to the OA requirement, and that makes all the difference in the world.
No publisher can block deposit; all they can do is embargo the date on which access to the deposit is set as Open Access (OA).
All REF submissions must be deposited immediately upon acceptance for publication — embargo or no embargo. The length of the allowable OA embargo, and exemptions from it, are an entirely separate matter.
Immediate-deposit allows a uniform mandate to be adopted by all institutions and funders, regardless of publisher OA embargo policy.
Once deposited, even if embargoed, access to an individual copy for research purposes can nevertheless be requested and provided on a one-to-one basis by one click each from the requestor to request and one click from the author to comply, thanks to the institutional repositories’ copy-request Button.
But only if — and when — the papers are deposited.
Sale, Arthur; Couture, Marc; Rodrigues, Eloy; Carr, Les and Harnad, Stevan (2014) Open Access Mandates and the “Fair Dealing” Button. In: Dynamic Fair Dealing: Creating Canadian Culture Online (Rosemary J. Coombe & Darren Wershler, Eds.). University of Toronto Press.