New legislation is currently being drafted in order to give the British Library and other such institutions the right to digitise orphan.
Copyright law reforms in pipeline after Royal Assent given to Enterprise and Regulatory Reform Bill
In terms of the British Library it is a national reference library similar to the Library of Congress in Washington DC, rather than a public library. There is a separate public library system in London with over 395 branches and over 17 million books. There is also a British Library site in the North of England at Boston Spa and a further five legal deposit libraries in the British Isles which include the National Library of Scotland, the National Library of Wales, Cambridge University Library, the Bodleian Library of the University of Oxford and Trinity College Library Dublin. Whilst London is also home to the National Archive, London Metropolitan Archives, the BBC Archive and part of the BFI Archive.
http://www.legaldeposit.org.uk/