The agreement signed between the Copyright Licensing Agency and the Department of Health is called CLA Licence Plus for the NHS in England.
If copies cannot be made under the CLA Licence Plus, NHS library staff may supply copies under terms of the Copyright, Designs and Patents Act of 1988, which was updated in 2014 to include digital as well as printed works.
CLA Licence Plus Copyright Fee Paid Articles
A reminder that all libraries covered by the CLA Licence for the NHS in England requiring articles needed for sharing by more than one person, which cannot be sourced within the NHS, may request Copyright Fee Paid (CFP) articles from the allocation included in the CLA Licence Plus. Once obtained, these articles may be treated as if owned by the NHS in England, and shared under the terms of the CLA Licence. Your library will not be charged for the cost of these articles.
CFP articles may be obtained from the British Library, from the Royal Society of Medicine Library, and now also from Reprints Desk. I understand from libraries who use Reprints Desk that they are very quick, and especially good for e-pubs ahead of print/pre-publication articles, so you may wish to try them out!
See below for information for obtaining CFP articles from all three sources: