National Libraries in the UK
National Libraries are collections which often hold the wealth of knowledge of that country or institution. They are often established by the government of that nation to serve as the preeminent repository of information for that country.
Very often it does mean that you are unable to borrow items as their collections can include numerous rare, valuable, or significant works. However you can often visit the library and with prior arrangement view items in that collection. The thing to do is contact the library before you visit to find out what arrangements need to be made.
The major National Libraries of the UK are:
National Art Library
National Library for Health
National Library of Scotland
National Library of Wales
There are also pages to help you search or find worldwide national libraries:
National Libraries Website
National Library Catalogues Worldwide