The SCONUL Access scheme, giving access to higher education libraries, is currently suspended. When the service is available again, you'll need to go to the SCONUL Access webpage to apply for membership.
University staff and students wishing to carry out research at the British Library are subject to their standard admissions criteria. Proof of home address (utility bill, bank statement, driving licence) and signature (credit card, passport, driving licence) are needed. Students may also be asked to present student ID cards.
Full details of how to apply for a reader's pass are available on the British Library web pages.