The British Library at St Pancras, London is a national research library. It does not lend books nor does it aim to stock multiple copies of basic text books. If your research needs are not fulfilled by other libraries, try searching the British Library catalogue. For more information and to register for a Reader Pass, please see the British Library website.
JISC's Library Hub Discover (formerly COPAC) is a joint catalogue of many national, university and research libraries in the UK and Ireland.
Find your local public library by entering your postcode on this online guide from the Government.
You can search the catalogue of the University of London's Library at Senate House which includes holdings of all their research institutes.