Wellcome Library http://wellcomelibrary.org/ : for historical material on East Asian medicine
Institutional libraries: even if you are no longer affiliated you may be able to get access as an alumnus or through being a student/staff elsewhere, or even sometimes just as a local inhabitant.
Local authority libraries: you can theoretically order anything through inter-library loan but the charge is no longer always negligible and the waiting time is very variable
Cochrane Library www.thecochranelibrary.com: you can freely (in the UK and many other countries) search the database of their own (highly regarded) systematic reviews
National Library for Health (formerly National Electronic Library for Health) www.library.nhs.uk: this was a very useful NHS resource that changed into a rather less useful NHS resource and now has disappeared altogether. The url takes you to a NICE website that provides resources that are largely accessible only to NHS personnel.